A triangle is in the shape of a 30 degrees minus 60 degrees minus 90 degrees right triangle. If the hypotenuse of the outer triangle is 25 ft, find the lengths of the legs of the triangle, in inches.

Question

Lily Hess

Mathematics

25 November, 14:19

A triangle is in the shape of a 30 degrees minus 60 degrees minus 90 degrees right triangle. If the hypotenuse of the outer triangle is 25 ft, find the lengths of the legs of the triangle, in inches.

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Answers (1)

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Stephen Nichols · Answer 1

150 inches 260 inches

Step-by-step explanation:

The sides of a 30°-60°-90° right triangle have the ratios ...

1 : √3 : 2

The shortest side is half the length of the hypotenuse, so is ...

(25 ft) (12 in/ft) = 150 in

The longer side is √3 times that length, so is about ...

(150 in) √3 ≈ 259.808 in

The legs of the triangle are 150 inches and about 260 inches.