Question

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

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:

$cos C=\dfrac{a^2+b^2-c^2}{2ab}$

$cos C=\dfrac{4^2+7^2-9^2}{2(4)(7)}$

$cos C=\dfrac{16+49-81}{56}$

$cos C=\dfrac{-16}{56}$

Taking cos inverse on both sides, we get

$C=cos^{-1} \dfrac{-16}{56}$

$C=106.60155$

$C\approx 106.6$

Therefore, the correct option is C.