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In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=37°, and SQ = 56 feet. Find the length of QR to the nearest tenth of a foot

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sqdancefan

Answer:

  70.1 ft

Step-by-step explanation:

The cosine relation gives the ratio of the adjacent side to the hypotenuse for an acute angle in a right triangle:

  Cos = Adjacent/Hypotenuse

  cos(37°) = SQ/QR

Rearranging gives ...

  QR = SQ/cos(37°) = (56 ft)/0.798636 = 70.1 ft

The length of QR is about 70.1 ft.

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