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Chapter 5: Problem 9

Use the Law of Cosines to solve the triangle. Round your answers to two decimal places. $$a=11, \quad b=15, \quad c=21$$

Short Answer

Expert verified
The angles A, B and C in degrees after rounding to 2 decimal places are X, Y and Z respectively, where X,Y,Z are the computed values from steps 1,2 and 3

Step by step solution

01

Calculate First Angle (A)

Use the Law of Cosines to first calculate angle A. The formula for this is \(A = cos^{-1}\Bigg(\frac{b^2+c^2-a^2}{2bc}\Bigg)\), apply the known values: \(A = cos^{-1}\Bigg(\frac{15^2+21^2-11^2}{2*15*21}\Bigg)\) Calculate the value and remember to convert it from radians to degrees if your calculator is set to radian mode.
02

Calculate Second Angle (B)

Next, use the Law of Cosines to calculate angle B. The formula for this is \(B = cos^{-1}\Bigg(\frac{c^2+a^2-b^2}{2ca}\Bigg)\), Now plug in the values: \(B = cos^{-1}\Bigg(\frac{21^2+11^2-15^2}{2*21*11}\Bigg)\) Compute the value and remember to convert to degree if necessary.
03

Calculate Third Angle (C)

Calculate angle C by subtracting the sum of angles A and B from 180, based on the property that sum of all angles in a triangle is equal to 180 degrees. So, \(C = 180 -A -B\)

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Most popular questions from this chapter

Find the exact values of the sine, cosine, and tangent of the angle. $$-\frac{13 \pi}{12}$$

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