Question

the shorter leg of a 30°-60°-90° triangle has a length of 8 feet. what is the length of the hypotenuse? write your answer in simplest radical form.
feet

Explanation:

Step1: Recall 30-60-90 triangle ratios

In a \(30^\circ - 60^\circ - 90^\circ\) triangle, the ratios of the sides are \(1:\sqrt{3}:2\) (shorter leg : longer leg : hypotenuse). The shorter leg is opposite the \(30^\circ\) angle, and the hypotenuse is twice the shorter leg.

Step2: Calculate hypotenuse length

Given the shorter leg length is 8 feet. Using the ratio, hypotenuse \(= 2\times\) shorter leg. So hypotenuse \(= 2\times8 = 16\) feet.

Answer:

16