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m_a_m_a [10]
2 years ago
15

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

Mathematics
1 answer:
sergiy2304 [10]2 years ago
4 0

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.

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