Question

In triangle ABC, AC=13, BC=84, and AB=85. Find the measure of angle C

Answer 1

Given:

In triangle $ABC, AC=13, BC=84, AB=85$.

To find:

The measure of angle C.

Solution:

Law of Cosines:

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

$\cos C=\dfrac{BC^2+AC^2-AB^2}{2(BC)(AC)}$

Substituting the given values, we get

$\cos C=\dfrac{(84)^2+(13)^2-(85)^2}{2(84)(13)}$

$\cos C=\dfrac{7056+169-7225}{2184}$

$\cos C=\dfrac{0}{2184}$

$\cos C=0$

Taking cos inverse on both sides, we get

$C=\cos^{-1}(0)$

$C=90^\circ$

Therefore, the measure of angle C is 90 degrees.