Question

find the measure of x.
14
48°
x =?
round to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the sine of an angle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, $\theta = 48^{\circ}$, the opposite side is $14$, and the hypotenuse is $x$. So, $\sin48^{\circ}=\frac{14}{x}$.

Step2: Solve for $x$

Rearrange the formula $\sin48^{\circ}=\frac{14}{x}$ to get $x=\frac{14}{\sin48^{\circ}}$.
We know that $\sin48^{\circ}\approx0.7431$.
Then $x=\frac{14}{0.7431}\approx18.84$.

Answer:

$18.84$