114k views
4 votes
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​

What is the measure of <C? Round your answer to the nearest tenth of a degree. A-example-1
User Shirker
by
7.2k points

1 Answer

5 votes

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.

User Sheo Narayan
by
7.2k points