Question

a buildings rafter forms the hypotenuse of a 30°-60°-90° triangle with the roofs frame. if the rafter measures 9 feet, then the short leg measures feet. 1 4.5 6 9

Explanation:

Step1: Recall 30-60-90 triangle ratios

In a \(30^\circ\)-\(60^\circ\)-\(90^\circ\) triangle, the sides are in the ratio \(1 : \sqrt{3} : 2\), where the side opposite \(30^\circ\) (short leg) is \(x\), the side opposite \(60^\circ\) (long leg) is \(x\sqrt{3}\), and the hypotenuse is \(2x\).

Step2: Relate hypotenuse to short leg

Given hypotenuse \(= 9\) feet, and hypotenuse \(= 2x\) (where \(x\) is short leg). So, \(2x = 9\).

Step3: Solve for short leg \(x\)

\(x=\frac{9}{2}=4.5\)

Answer:

4.5