What is the value of x? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth. x = ft A scalene triangle M N P. Side N P is labeled as 15 feet. Side M P is labeled as x. Angle N is labeled as 61 degrees. Angle P is labeled as 38 degrees.

Question

Mathematics

Blossom

17 October, 09:03

What is the value of x? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth. x = ft A scalene triangle M N P. Side N P is labeled as 15 feet. Side M P is labeled as x. Angle N is labeled as 61 degrees. Angle P is labeled as 38 degrees.

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Answers (1)

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Mariam · Answer 1

13.3 ft

Step-by-step explanation:

We are being asked to find an unknown side length in a triangle with two given angles and the side between them. The law of sines is applicable, but we need to know the angle opposite the given side.

Angle M has a value that makes the sum of angles be 180°, so it is ...

∠M = 180° - 61° - 38° = 81°

The law of sines tells you the length of side MP is ...

MP = NP·sin (N) / sin (M) = (15 ft) ·sin (61°) / sin (81°)

x = MP ≈ 13.3 ft