Question

find the side labeled x.
x =
3
x
30°

Explanation:

Step1: Recall sine - function definition

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 3, and the hypotenuse has length $x$.
So, $\sin30^{\circ}=\frac{3}{x}$.

Step2: Substitute the value of sine

We know that $\sin30^{\circ}=\frac{1}{2}$. So, the equation becomes $\frac{1}{2}=\frac{3}{x}$.

Step3: Solve for x

Cross - multiply to get $x\times1 = 2\times3$.

Answer:

$x = 6$