Question

a 30 - 60 - 90 triangle has a hypotenuse with a length of 10 feet. what are the lengths of the short leg and the medium leg? select two answers, one for each leg. the short leg has a length of 5 ft. the medium leg has a length of 8.66 ft. the medium leg has a length of 5.77 ft. the short leg has a length of 7.07 ft. the short leg has a length of 5.77 ft. the medium leg has a length of 9.24 ft.

Explanation:

Step1: Recall 30 - 60 - 90 triangle ratio

In a 30 - 60 - 90 triangle, if the hypotenuse is $c$, the short - leg (opposite the 30 - degree angle) is $a=\frac{c}{2}$, and the medium - leg (opposite the 60 - degree angle) is $b = a\sqrt{3}$.

Step2: Calculate the length of the short leg

Given $c = 10$ feet. Using the formula $a=\frac{c}{2}$, we have $a=\frac{10}{2}=5$ feet.

Step3: Calculate the length of the medium leg

Since $a = 5$ feet, and $b=a\sqrt{3}$, then $b = 5\sqrt{3}\approx5\times1.732 = 8.66$ feet.

Answer:

The short leg has a length of 5 ft.
The medium leg has a length of 8.66 ft.