Question

find the missing side labeled with x using trigonometry.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Let's assume the angle is $54^{\circ}$ and the hypotenuse is $15$. The side labeled $x$ is the opposite side to the $54^{\circ}$ angle.

Step2: Apply the sine formula

We have $\sin(54^{\circ})=\frac{x}{15}$. Then $x = 15\times\sin(54^{\circ})$.
Since $\sin(54^{\circ})\approx0.8090$, we get $x=15\times0.8090 = 12.135\approx12.4$ (rounded to one decimal place).

Answer:

$12.4$