Question

the hypotenuse of a $30^\circ$-$60^\circ$-$90^\circ$ triangle measures 10 inches. which could be the length of a leg of the triangle? select all that apply.a. 6b. 8c. 5d. $5\sqrt{3}$

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 shortest leg (opposite $30^\circ$) is half the hypotenuse, and the longer leg (opposite $60^\circ$) is $\sqrt{3}$ times the shortest leg.

Step2: Calculate shortest leg length

Shortest leg $= \frac{1}{2} \times \text{hypotenuse}$
$\frac{1}{2} \times 10 = 5$

Step3: Calculate longer leg length

Longer leg $= \text{shortest leg} \times \sqrt{3}$
$5 \times \sqrt{3} = 5\sqrt{3}$

Answer:

C. 5
D. $5\sqrt{3}$