Question

if the shortest leg in the following 30° - 60° - 90° triangle has length 17 meters, what are the lengths of the other leg and the hypotenuse? enter the exact, fully simplified answers.

Explanation:

Step1: Identify the short - leg length

The shortest leg of a 30 - 60 - 90 triangle corresponds to the side opposite the 30° angle. Given $x = 17$ meters.

Step2: Find the length of the other leg

The other leg (opposite the 60° angle) has length $\sqrt{3}x$. Substitute $x = 17$ into $\sqrt{3}x$, we get $17\sqrt{3}$ meters.

Step3: Find the length of the hypotenuse

The hypotenuse has length $2x$. Substitute $x = 17$ into $2x$, we get $2\times17=34$ meters.

Answer:

The length of the other leg is $17\sqrt{3}$ meters and the length of the hypotenuse is 34 meters.