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Chapter 5: Problem 13

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 measure of Angle A is approximately 38.21 degrees, Angle B is about 70.53 degrees, and Angle C is roughly 71.26 degrees. Round all answers to two decimal places.

Step by step solution

01

Find Angle A

Using the formula for the cosine of angle A (\( \cos(A) = \frac{b^2 + c^2 - a^2}{2bc} \)) and given side lengths a=11, b=15, c=21, first substitute these values into the formula. Then, find the arc cosine (inverse of cosine) of the result in order to find the degree measure of angle A. This will give us the value for angle A in degrees, which we can round to two decimal places.
02

Find Angle B

Next, solve for angle B using the formula \( \cos(B) = \frac{a^2 + c^2 - b^2}{2ac} \). Replace a, b, and c with their respective values. Compute the arc cosine of the result to find the measure of angle B in degrees, and round to two decimal places.
03

Find Angle C

Finally, solve for angle C. Use the formula \( \cos(C) = \frac{a^2 + b^2 - c^2}{2ab} \) and substitute the given side lengths. Compute the arc cosine to get angle C in degrees. Alternatively, considering that the sum of angles in a triangle is 180 degrees, one can calculate angle C by subtracting the already known angles A and B from 180. Round the result to two decimal places if necessary.

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