Question

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°

Answer 1

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.