Question

A right triangle is shown. The height and length of the hypotenuse are unknown and the length other side is 5 feet. The other angles measure 60 and 30 degrees.
From the side view, a gymnastics mat forms a right triangle with other angles measuring 60° and 30°. The gymnastics mat extends 5 feet across the floor. How high is the mat off the ground?

Five-halves ft
StartFraction 5 StartRoot 3 EndRoot Over 3 EndFraction ft
5 StartRoot 3 EndRoot
10

Answer 1

5√3/3 ft

Reason: In a 30°-60°-90° triangle the legs are in ratio 1 : √3 (short opposite 30°, long opposite 60°). The mat's 5-ft floor length is the long leg, so the height (short leg) = 5 / √3 = 5√3/3 ft.