By clicking Accept all cookies, you agree Stack Exchange can store cookies on your device and disclose information in accordance with our Cookie Policy. sinc sinb To calculate the area of an equilateral triangle, you only need to have the side given: area = a * 3 / 4. which is impossible, and so\(\beta48.3\). It appears that there may be a second triangle that will fit the given criteria. We can stop here without finding the value of\(\alpha\). We will investigate three possible oblique triangle problem situations: ASA (angle-side-angle) We know the measurements of two angles and the included side. K634: Use the Sine Rule to Find Acute Angles in Non Right-Angled Triangles.. "/> A triangles with one 90 degrees angle are called a right triangles. What is the area of one of the, Amy needs to order a shade for a triangular-shaped window that has. Is // really a stressed schwa, appearing only in stressed syllables? How would I go about finding an angles of a non-right angled triangle when given the area and two of its sides. This gives, \[\begin{align*} \alpha&= 180^{\circ}-85^{\circ}-131.7^{\circ}\\ &\approx -36.7^{\circ} \end{align*}\]. If you know one leg a and the hypotenuse c, use the formula: area = a (c - a) / 2. The angle supplementary to\(\beta\)is approximately equal to \(49.9\), which means that \(\beta=18049.9=130.1\). ASA - a side and 2 adjacent angles. Determine the number of triangles possible given \(a=31\), \(b=26\), \(\beta=48\). \Rightarrow \sin C & = 8.06 Will SpaceX help with the Lunar Gateway Space Station at all? The functions of sine, cosine, and tangents, can only be used to find the area of a triangle with an acute angle. bsin = asin ( 1 ab)(bsin) = (asin)( 1 ab) Multiply both sides by 1 ab. To find the remaining missing values, we calculate \(\alpha=1808548.346.7\). To find\(\beta\),apply the inverse sine function. An acute right angle triangle is not possible because one of the internal angle of right triangle is always 90 degrees. Find the size of Angle $C$. It is given as: A + B + C = 180. It only takes a minute to sign up. The area formula states: Area of triangle = One is triangle and and other one is rectangle. This is equivalent to one-half of the product of two sides and the sine of their included angle. The cosine rule states: Area Formula The area of a triangle can be found given the lengths of two sides and the angle between them. Instead, we can use the fact that the ratio of the measurement of one of the angles to the length of its opposite side will be equal to the other two ratios of angle measure to opposite side. The diagram shown in Figure \(\PageIndex{17}\) represents the height of a blimp flying over a football stadium. 6. Because the range of the sine function is\([ 1,1 ]\),it is impossible for the sine value to be \(1.915\). Finding the Area of a Right Triangle: Area of right triangle = ()bh square units Substituting the values in the formula, we get A = ()815 cm 2 A = 415 cm 2 A = 60 cm 2 Therefore, the area of the right triangle is 60 cm 2. Area =s(sa)(sb)(sc) Area = s ( s a) ( s b) ( s c) Which means, she forgot to multiply the product of base and height by 1/2. For the triangle shown, side is the base and side is the height. The sixth-grade art students aremaking a mosaic using tiles in the shapeof right triangle. Area of non right angled triangles; Cosine Rule . Round your answers to the nearest tenth. \(\dfrac{\sin\alpha}{a}=\dfrac{\sin\beta}{b}=\dfrac{\sin\gamma}{c}\). However, you don't need to know the length of the hypotenuse to find the area of any triangle with a right angle. Previous Area of a Trapezium Practice Questions. \[\begin{align*} Area&= \dfrac{1}{2}ab \sin \gamma\\ Area&= \dfrac{1}{2}(90)(52) \sin(102^{\circ})\\ Area&\approx 2289\; \text{square units} \end{align*}\]. h = bsin and h = asin. Apart from the above formula, we have Heron's formula to calculate the triangle's area when we know the length of its three sides. To find the elevation of the aircraft, we first find the distance from one station to the aircraft, such as the side\(a\), and then use right triangle relationships to find the height of the aircraft,\(h\). This will give you the area of the triangle in square units. How do I find the area of a right triangle given sides? If SAS is Solve the triangle shown in Figure 10.1.7 to the nearest tenth. Entering sides of values 1.00, 2.00, and 2.00 will yield much more acurate results of 75.5, 75.5, and 29.0. answer 10.7 alternatives 10.7square cm 10.7 square cm Question 5 120 seconds Q. AB=3.2cm, BC=8.4cm, area of the tringle ABC is 10 cm 2. Click here for Answers. An alternate formula for the area of a triangle. How are the precise angles of a triangle found in terms of $\pi$ when the sides are given? There are three possible cases: ASA, AAS, SSA. Round your answers to the nearest tenth. or, based on the units given, 42 square centimeters. Multiply the two values together, then multiply their product by . The angle used in calculation is\(\alpha\),or\(180\alpha\). Depending on the information given, we can choose the appropriate equation to find the requested solution. Now that we know\(a\),we can use right triangle relationships to solve for\(h\). The cosine rule is concerned with triangles where the lengths of two sides and the angle between them, or the lengths of three sides, are given. Set up the formula for the area of a triangle. If there is more than one possible solution, show both. \[\begin{align*} \dfrac{\sin(130^{\circ})}{20}&= \dfrac{\sin(35^{\circ})}{a}\\ a \sin(130^{\circ})&= 20 \sin(35^{\circ})\\ a&= \dfrac{20 \sin(35^{\circ})}{\sin(130^{\circ})}\\ a&\approx 14.98 \end{align*}\]. What error did Monica, Actual area of the triangular piece of fabric is 45 square inches. Here in the right angle triangle, the three sides are known as the base, the altitude, and the hypotenuse. To check the solution, subtract both angles, \(131.7\) and \(85\), from \(180\). In the triangle $ABC$, $a = 5$, $b = 6$ and the area is $11~\text{cm}^2$. What is the area of the shade ? Wayne's house in the above picture is made up of using two shapes. The LibreTexts libraries arePowered by NICE CXone Expertand are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Success Criteria Know and apply the sine rule and cosine rule a 2 = b 2 + c 2 - 2bcCosA to find unknown lengths and angles. Given \(\alpha=80\), \(a=120\),and\(b=121\),find the missing side and angles. Plug the base and height into the formula. Area = 0.5 * width * height; In the next line, We are calculating the other side of a right angled triangle using the Pythagoras formula C = a + b, which is similar to C = a+b. The two sides that meet to, form a right angle are 3 centimeters and 5, centimeters long. sin a = sin c and sin b = sin c. Collectively, these relationships are called the Law of Sines. Connect and share knowledge within a single location that is structured and easy to search. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. \(\dfrac{a}{\sin\alpha}=\dfrac{b}{\sin\beta}=\dfrac{c}{\sin\gamma}\). Observing the two triangles in Figure \(\PageIndex{15}\), one acute and one obtuse, we can drop a perpendicular to represent the height and then apply the trigonometric property \(\sin \alpha=\dfrac{opposite}{hypotenuse}\)to write an equation for area in oblique triangles. We then set the expressions equal to each other. To subscribe to this RSS feed, copy and paste this URL into your RSS reader. The area for our case is equal to 11.25 in. Cosine rule subject assignment point assignmentpoint. Khan Academy is a 501(c)(3) nonprofit organization. Area = base height. Monica says that the area ofthe fabric is 90 square inches . There are many trigonometric applications. MathJax reference. The distance from one station to the aircraft is about \(14.98\) miles. The Law of Sines can be used to solve triangles with given criteria. Knowing how to approach each of these situations enables us to solve oblique triangles without having to drop a perpendicular to form two right triangles. Therefore, the legs or catheti are also two heights of the triangle. The Law of Sines can be used to solve oblique triangles, which are non-right triangles. This formula is derived from the area of a triangle formula, A=1/2Bh For any triangle ABC with side a opposite A, side b opposite B and side c opposite C, height h is represented by a line perpendicular to the base of the triangle. Solve the triangle in Figure \(\PageIndex{10}\) for the missing side and find the missing angle measures to the nearest tenth. Because you are trying to find C alone. Try sides equal to 1,2,2. This task can be resolved using the ASA rule. Area Formula for Non-Right Triangles. (Remember that the sine function is positive in both the first and second quadrants.) Watch our triangle area calculator performing all calculations for you! (method below), \begin{align*} C. The area of each triangle will be 56 square meters divided by 2. Area of a right angled triangle is: 15.00. My professor says I would not graduate my PhD, although I fulfilled all the requirements, Guitar for a patient with a spinal injury. Replacing l and w with the Base and Height in equation (1), we obtain: Using the pronumerals A for area, b for base and h for height, we can write the formula for the area of a right-angled . To find an unknown side, we need to know the corresponding angle and a known ratio. trigonometry; Site design / logo 2022 Stack Exchange Inc; user contributions licensed under CC BY-SA. It is important to verify the result, as there may be two viable solutions, only one solution (the usual case), or no solutions. 2014 BestMaths. Jay Abramson (Arizona State University) with contributing authors. But Monica says that area of the fabric is 90 square inches. See Example \(\PageIndex{4}\). According to the Law of Sines, the ratio of the measurement of one of the angles to the length of its opposite side equals the other two ratios of angle measure to opposite side. Some are flat, diagram-type situations, but many applications in calculus, engineering, and physics involve three dimensions and motion. In any triangle, we can draw an altitude, a perpendicular line from one vertex to the opposite side, forming two right triangles. The height of thetriangle is 15 inches and the triangles baseis 6 inches. \[\begin{align*} \beta&= {\sin}^{-1}\left(\dfrac{9 \sin(85^{\circ})}{12}\right)\\ \beta&\approx {\sin}^{-1} (0.7471)\\ \beta&\approx 48.3^{\circ} \end{align*}\], In this case, if we subtract \(\beta\)from \(180\), we find that there may be a second possible solution. triangle right non angle area formula chinatsu arch1392. The sine rule is concerned with triangles where pairs of angles and their opposite sides are given. Subject: Mathematics. We then set the expressions equal to each other. Area of Triangle inside a Circle in terms of angle and radius, If $AB = 9$ and $AC:BC=40:41$, then find maximum area of $\triangle ABC$. See Example \(\PageIndex{5}\). Alternatively, if you know the three vertices (x1,y1), (x2,y2) and (x3,y3) then the area is given by the formula: A = 1 2|x1y2 +x2y3 + x3y1 x1y3 x2y1 x3y2| Also, trigonometric functions are used to find the area when we know two sides and the angle . However, in the obtuse triangle, we drop the perpendicular outside the triangle and extend the base\(b\)to form a right triangle. A planet you can take off from, but never land back. The Moon turns into a black hole of the same mass -- what happens next? Maths revision video and notes on the topic of trigonometry, finding the area of non right angled triangles. So we get: Area = (c) (b sin A) Which can be simplified to: Area = 12 bc sin A. In order to find the area of a right angled triangle: 1 Identify the height and base length of your triangle (you might need to calculate these values) 2 Write the formula A = 1 2bh A = 1 2 b h 3 Substitute the values for base and height 4 Calculate How to find the area of a right angled triangle Right angle triangle worksheet Lets see how this statement is derived by considering the triangle shown in Figure \(\PageIndex{5}\). All proportions will be equal. Round the area to the nearest integer. These triangles have measurements as, shown in the diagram. This is the error that she has made. AAS - a side, 1 adjacent angle, and the opposite angle. Learn how to use trigonometry in order to find missing sides and angles in any triangle. Solving for\(\gamma\), we have, \[\begin{align*} \gamma&= 180^{\circ}-35^{\circ}-130.1^{\circ}\\ &\approx 14.9^{\circ} \end{align*}\], We can then use these measurements to solve the other triangle. \(Area=\dfrac{1}{2}(base)(height)=\dfrac{1}{2}b(c \sin\alpha)\), \(Area=\dfrac{1}{2}a(b \sin\gamma)=\dfrac{1}{2}a(c \sin\beta)\), The formula for the area of an oblique triangle is given by. A right-angled triangle or a right triangle has one of its angles at 90 and the other two angles compose a sum of 90. How is lift produced when the aircraft is going down steeply? However, we were looking for the values for the triangle with an obtuse angle\(\beta\). How can I design fun combat encounters for a party traveling down a river on a raft? Trig challenge problem: area of a hexagon Our mission is to provide a free, world-class education to anyone, anywhere. [1] 3. Round the area to the nearest tenth. \[\begin{align*} \dfrac{\sin \alpha}{10}&= \dfrac{\sin(50^{\circ})}{4}\\ \sin \alpha&= \dfrac{10 \sin(50^{\circ})}{4}\\ \sin \alpha&\approx 1.915 \end{align*}\]. Where A , B, and C are the internal angles of a triangle. Visit Our Website: http://www.vividmath.com For Full Video Lessons My Channel: http://www.youtube.com/user/vividmaths?feature=mheeFind Me On: Facebook:h. We will use this proportion to solve for\(\beta\). But Monica says that. The method depends on which sides you're given: If you know the two legs, then use the formula area = a b / 2, where a, and b are the legs. 17 Images about Chinatsu-ARCH1392 : Chinatsu-ARCH1392, Chinatsu-ARCH1392 and also Trigonometry in Right Angled Triangles I.mp4 - YouTube. Find the altitude of the aircraft in the problem introduced at the beginning of this section, shown in Figure \(\PageIndex{16}\). ;-). Area of an equilateral triangle. or, in an alternative form for use when finding angle sizes: The cosine rule is concerned with triangles where the lengths of two sides and the angle between them, or the lengths of three sides, are given. Know and apply the formula for the area of a triangle to calculate the area, sides or angles of any triangle. Making statements based on opinion; back them up with references or personal experience. Explanation: The formula for the area of a triangle is. We know that angle \(\alpha=50\)and its corresponding side \(a=10\). Id prefer a solution that I can code into a function, or something that does not require constructing right triangles from it. Accessibility StatementFor more information contact us atinfo@libretexts.orgor check out our status page at https://status.libretexts.org. where is the base of the triangle and is the height. \sin C & = \frac{11^2 \cdot 2}{5 \cdot 6}\\ The formula used to find the radius is, R = (abc) / (4K), where K is the area of the triangle. \[\begin{align*} \sin(15^{\circ})&= \dfrac{opposite}{hypotenuse}\\ \sin(15^{\circ})&= \dfrac{h}{a}\\ \sin(15^{\circ})&= \dfrac{h}{14.98}\\ h&= 14.98 \sin(15^{\circ})\\ h&\approx 3.88 \end{align*}\]. If there is more than one possible solution, show both. Therefore: Height of the triangle = Width of the rectangle. This is because of the opposite length, the right angle is the hypotenuse, and the other two sides are the cathetus. To find the area of the triangle, you must multiply the hypotenuse's two adjacent sides: the base and the height. How to Calculate the Angles of a Triangle. \[\begin{align*} \dfrac{\sin(50^{\circ})}{10}&= \dfrac{\sin(30^{\circ})}{c}\\ c\dfrac{\sin(50^{\circ})}{10}&= \sin(30^{\circ})\qquad \text{Multiply both sides by } c\\ c&= \sin(30^{\circ})\dfrac{10}{\sin(50^{\circ})}\qquad \text{Multiply by the reciprocal to isolate } c\\ c&\approx 6.5 \end{align*}\]. The aircraft is at an altitude of approximately \(3.9\) miles. Area of a non right angled triangle lesson. or. or , in alternative form for finding angles: The area of a triangle can be found given the lengths of two sides and the angle between them. rev2022.11.10.43024. How to find an angle of a non-right angle triangle when given two sides and an area? From this, we can determine that, \[\begin{align*} \beta &= 180^{\circ} - 50^{\circ} - 30^{\circ}\\ &= 100^{\circ} \end{align*}\]. 0.5 x a x c Sin B. See Figure \(\PageIndex{4}\). Sine Law For Non-right Angle Triangles - GeoGebra www.geogebra.org. Next Mean, Mode, Median, Range Practice Questions. \[\begin{align*} \dfrac{\sin(85)}{12}&= \dfrac{\sin(46.7^{\circ})}{a}\\ a\dfrac{\sin(85^{\circ})}{12}&= \sin(46.7^{\circ})\\ a&=\dfrac{12\sin(46.7^{\circ})}{\sin(85^{\circ})}\\ &\approx 8.8 \end{align*}\], The complete set of solutions for the given triangle is, \(\begin{matrix} \alpha\approx 46.7^{\circ} & a\approx 8.8\\ \beta\approx 48.3^{\circ} & b=9\\ \gamma=85^{\circ} & c=12 \end{matrix}\). Solving both equations for\(h\) gives two different expressions for\(h\). Finding the Area of an Obtuse Triangle. Terms of Use | They can often be solved by first drawing a diagram of the given information and then using the appropriate equation. From this, we can determine that = 180 50 30 = 100 To find an unknown side, we need to know the corresponding angle and a known ratio. Obviously using both a tangent calculator and an exponent calculator is quite helpful. Any triangle that is not a right triangle is an oblique triangle. Click Create Assignment to assign this modality to your LMS. Each triangularface of the Pyramid of Peace inKazakhstan is made up of 25 smaller equilateraltriangles. Hyperbolic Functions. Median m a . Area of a right-angled triangle = 1/2 Base Height: When it is an equilateral triangle and one side is given. % Progress How can we determine the altitude of the aircraft? Solving using the area of a triangle formula c 2 / (2 * (tan -1 + tan -1 )) = 225 / (2 * (0.577350 -1 + 1.732051 -1 )) = 48.7 square feet. This is the error that she has made. \end{align*}. Because the angles in the triangle add up to \(180\) degrees, the unknown angle must be \(1801535=130\). What is the area that will be painted? Khan Academy is a 501(c)(3) nonprofit organization. boat trigonometry law right non triangles algebra cosines triangle figure port miles degrees angle travels far precalculus link shown another, pythagorean theorem triangle squares right area square sides shmoop hypotenuse geometry sum legs cm, formulas triangle geometry formula area input base height its, angle triangle missing right using triangles finding ratios trigonometric solving solve sbv, sohcahtoa sine cosine tangent transcript lesson, right angled non trigonometry pdf tes resources kb, cosine rule subject assignment point assignmentpoint, triangle right non angle area formula arch1392 chinatsu, Trigonometry introductory. Recall that the area formula for a triangle is given as Area = 1 2 b h, where b is base and h is height. In fact, inputting \({\sin}^{1}(1.915)\)in a graphing calculator generates an ERROR DOMAIN. Use the Law of Sines to solve for\(a\)by one of the proportions. In this section, we will find out how to solve problems involving non-right triangles. Collectively, these relationships are called the Law of Sines. Using the formula, Area of a Triangle, A = 1/2 b h. = 1/2 4 (cm) 3 (cm) = 2 (cm) 3 (cm) = 6 cm 2. What error did Monicamake ? The two sides that meet toform a right angle are 3 centimeters and 5 centimeters long. formulas. HAESE Mathematics Core Topics HL TEXTBOOK8. Heron of Alexandria was a geometer who lived during the first century A.D. In this case, we know the angle,\(\gamma=85\),and its corresponding side\(c=12\),and we know side\(b=9\). Other side of right angled triangle is: 7.81. If p, q and r are hypotenuses, adjacent, and the opposite of a right-angles triangle, then: p2 = r2 + q2. Explain your answer. Non-right angled triangle trigonometryA The unit circleB The area of a triangleC The cosine ruleD The sine ruleE. Similarly, we can compare the other ratios. Area of rectangle = l w = 2 (Area of one right triangle) This gives, Area of one right triangle = 1/2 l w. We usually represent the legs of the right-angled triangle as base and height. c = Math.sqrt ( (width * width) + (height * height)); In the next line . Download for free athttps://openstax.org/details/books/precalculus. square centimeters. This page titled 10.1: Non-right Triangles - Law of Sines is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request. Solution: Given: By changing the labels on the triangle we can also get: Area = ab sin C; Area = ca sin B; One more example: The lengths of the sides of a triangle are 4.2cm, 5.3cm and 7.6cm. Area of a Right Angled Triangle. 45-45-90 triangle: The 45-45-90 triangle, also referred to as an isosceles right triangle, since it has two sides of equal lengths, is a right triangle in which the sides corresponding to the angles, 45-45-90, follow a ratio of 1:1: . Find the area of a triangle with sides \(a=90\), \(b=52\),and angle\(\gamma=102\). Area of a Triangle Using Sine We can use sine to determine the area of non-right triangles. This type of triangle can be used to evaluate trigonometric functions for multiples of /6. We know that angle = 50 and its corresponding side a = 10 . Area equals half the product of two sides and the sine of the included angle. }\\ \dfrac{9 \sin(85^{\circ})}{12}&= \sin \beta \end{align*}\]. Correct answer: square centimeters. See Figure \(\PageIndex{6}\). Thus, the formula for the area of a right triangle is, Area of a right triangle = 1/2 base height. For triangles without a right angle, the sine rule, the cosine rule and the area formula can be used to solve triangles and find their areas. Use MathJax to format equations. Given a triangle with angles and opposite sides labeled as in Figure \(\PageIndex{6}\), the ratio of the measurement of an angle to the length of its opposite side will be equal to the other two ratios of angle measure to opposite side. According to the Law of Sines, the ratio of the measurement of one of the angles to the length of its opposite side equals the other two ratios of angle measure to opposite side. The Law of Sines is based on proportions and is presented symbolically two ways. The area of a right triangle can be found using the formula A = bh. Area of a triangle trig is a formula to calculate the area of any triangle: Area of triangle = 1 2 absinC Area of triangle = 1 2 a b sin C Previously, we have calculated the area of a triangle using another formula: Area of a triangle = base height 2 Area of a triangle = base height 2 How would I go about finding an angles of a non-right angled triangle when given the area and two of its sides. See Example \(\PageIndex{2}\) and Example \(\PageIndex{3}\). Are you familiar with the area formula $A = \frac{1}{2}ab\sin\gamma$? The general area formula for triangles translates to oblique triangles by first finding the appropriate height value. (via Brilliant), Find the other side lengths of a triangle given the perimeter, one side and an angle. Since\(\beta\)is supplementary to\(\beta\), we have, \[\begin{align*} \gamma^{'}&= 180^{\circ}-35^{\circ}-49.5^{\circ}\\ &\approx 95.1^{\circ} \end{align*}\], \[\begin{align*} \dfrac{c}{\sin(14.9^{\circ})}&= \dfrac{6}{\sin(35^{\circ})}\\ c&= \dfrac{6 \sin(14.9^{\circ})}{\sin(35^{\circ})}\\ &\approx 2.7 \end{align*}\], \[\begin{align*} \dfrac{c'}{\sin(95.1^{\circ})}&= \dfrac{6}{\sin(35^{\circ})}\\ c'&= \dfrac{6 \sin(95.1^{\circ})}{\sin(35^{\circ})}\\ &\approx 10.4 \end{align*}\]. Work through each of the proofs with the students on the main whiteboard. \[\begin{align*} \dfrac{\sin(85^{\circ})}{12}&= \dfrac{\sin \beta}{9}\qquad \text{Isolate the unknown. . There are three possible cases that arise from SSA arrangementa single solution, two possible solutions, and no solution. Why does "new" go before "huge" in: New huge Japanese company? Heron's Formula Heron's formula finds the area of oblique triangles in which sides a,b, a, b, and c c are known. Students take notes of the steps involved and try it for themselves after my work has been erased. You can use Heron's Formula to find the area of the triangle, even if you only know the sides of the triangle and not any of the angles (which is called SSS, or side-side-side, in trigonometry terms). Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here. Therefore, the area is equal to. The three angles must add up to 180 degrees. Find the area of the triangle given \(\beta=42\),\(a=7.2ft\),\(c=3.4ft\). \[\begin{align*} \dfrac{\sin(50^{\circ})}{10}&= \dfrac{\sin(100^{\circ})}{b}\\ b \sin(50^{\circ})&= 10 \sin(100^{\circ})\qquad \text{Multiply both sides by } b\\ b&= \dfrac{10 \sin(100^{\circ})}{\sin(50^{\circ})}\qquad \text{Multiply by the reciprocal to isolate }b\\ b&\approx 12.9 \end{align*}\], Therefore, the complete set of angles and sides is, \(\begin{matrix} \alpha=50^{\circ} & a=10\\ \beta=100^{\circ} & b\approx 12.9\\ \gamma=30^{\circ} & c\approx 6.5 \end{matrix}\). The area of any other triangle can be found with the formula below. Now, only side\(a\)is needed. Round the altitude to the nearest tenth of a mile. Textbook content produced byOpenStax Collegeis licensed under aCreative Commons Attribution License 4.0license. Book: Algebra and Trigonometry (OpenStax), { "10.1E:_Non-right_Triangles_-_Law_of_Sines_(Exercises)" : "property get [Map MindTouch.Deki.Logic.ExtensionProcessorQueryProvider+<>c__DisplayClass226_0.
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