Question

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

Answer 1

eason

Explanation:

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eason

Explanation:

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eason

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eason

Explanation:

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eason

Explanation:

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eason

Explanation:

boy

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Answer 2

Given:

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

To find:

The measure of angle C.

Solution:

Law of Cosines:

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

`\cos C=(BC^2+AC^2-AB^2)/(2(BC)(AC))`

Substituting the given values, we get

`\cos C=((84)^2+(13)^2-(85)^2)/(2(84)(13))`

`\cos C=(7056+169-7225)/(2184)`

`\cos C=(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.