Question

solve for x.
8
x
30
8√2
8√3
8
16

Explanation:

Step1: Identify trigonometric relation

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 30^{\circ}$, the opposite side to the $30^{\circ}$ angle has length 8, and the hypotenuse has length $x$. So, $\sin30^{\circ}=\frac{8}{x}$.

Step2: Recall the value of $\sin30^{\circ}$

We know that $\sin30^{\circ}=\frac{1}{2}$. So, the equation becomes $\frac{1}{2}=\frac{8}{x}$.

Step3: Solve for $x$

Cross - multiply: $x\times1 = 8\times2$. So, $x = 16$.

Answer:

D. 16