Triangle ABC has side lengths a=74.1, b= 60.8, c=114.2. What is the measure of angle C? a. 35.9° b. 28.8° c. 96.4° d. 115.3°

Question

asked Jan 1, 2022 56.9k views

1 Answer

Deeplovepan · Answer 1 · 2022-01-05T13:19:40+0000

Given:

In triangle ABC, a=74.1, b= 60.8, c=114.2.

To find:

The measure of angle C.

Solution:

According to the Law of cosine:

$\cos C=(a^2+b^2-c^2)/(2ab)$

Substituting
a=74.1,b= 60.8,c=114.2 , we get

$\cos C=((74.1)^2+(60.8)^2-(114.2)^2)/(2(74.1)(60.8))$

$\cos C=(5490.81+3696.64-13041.64)/(9010.56)$

$\cos C=(-3854.19)/(9010.56)$

$\cos C=-0.42774145$

Taking cos inverse on both sides, we get

$C=\cos^(-1){-0.42774145}$

C=115.324312

$C=115.3^\circ$

Therefore, the correct option is d.