Question

What is the measure of <C? Round your answer to the nearest tenth of a degree.

A 73.4
B 74.1
C 106.6
D 100.7​

Answer 1

Given:

In triangle
`ABC, AB=9,BC=4,AC=7`.

To find:

The measure of angle C.

Solution:

We have,
`AB=9,BC=4,AC=7`. It means
`c=9,a=4,b=7`.

According to the law of cosines:

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

`cos C=(4^2+7^2-9^2)/(2(4)(7))`

`cos C=(16+49-81)/(56)`

`cos C=(-16)/(56)`

Taking cos inverse on both sides, we get

`C=cos^(-1) (-16)/(56)`

`C=106.60155`

`C\approx 106.6`

Therefore, the correct option is C.