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

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asked Jul 3, 2022 51.4k views

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Corey Wu · Answer 1 · 2022-07-05T07:09:34+0000

Answer:

eason

Explanation:

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eason

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eason

Explanation:

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eason

Explanation:

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eason

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eason

Explanation:

boy

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Shadox · Answer 2 · 2022-07-09T06:49:52+0000

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.

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

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