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Solve for x in the triangle.

Solve for x in the triangle.-example-1

1 Answer

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Answer:

D. 87

Explanation:

You want to know the measure of the angle opposite the longest side in a triangle with side lengths 13, 16, and 20 inches.

Angle relations

The angle x is opposite the side of length 20 inches in this triangle, which is the longest side. That tells you x is the largest angle.

The largest angle in any triangle is never less than 60°. This eliminates all answer choices except the last one:

x = 87

Law of Cosines

If you want to go to the trouble to solve the triangle, the law of cosines is helpful. For sides a, b, c and angle C, it tells you ...

c² = a² +b² -2ab·cos(C)

Solving for the angle, we have ...

C = arccos((a² +b² -c²)/(2ab))

C = arccos((13² +16² -20²)/(2·13·16)) = arccos(25/416) ≈ 86.55°

x ≈ 87

User Miguel Peniche
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