Question

question 8 of 25
in the 30-60-90 triangle below, side s has a length of ___ and side q has a length of ___.

a. 4, 8√3
b. 16√3, 16√3
c. 4√2, 4√2
d. 4, 4√3
e. 16√3, 5
f. 8√3, 16

Explanation:

Step1: Identify hypotenuse length

The hypotenuse (side $s$) is given as 8.

Step2: Find short leg (side opposite 30°)

In a 30-60-90 triangle, the short leg is half the hypotenuse.
$\text{Short leg } = \frac{1}{2} \times 8 = 4$
This short leg corresponds to side $s$ (wait correction: reorient triangle: the side opposite 30° is the shortest side, which is the side labeled as the base (let's confirm: 30° angle's opposite side is the side labeled as the base, hypotenuse is the side marked 8. So side $s$ (base, opposite 30°) is $\frac{8}{2}=4$.

Step3: Find long leg (side $q$)

In a 30-60-90 triangle, the long leg is short leg $\times \sqrt{3}$.
$q = 4 \times \sqrt{3} = 4\sqrt{3}$

Answer:

D. $4, 4\sqrt{3}$