Question

find the measure of x. round to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 48^{\circ}\), the opposite side \(a = 14\), and the hypotenuse is \(x\). So, \(\sin48^{\circ}=\frac{14}{x}\).

Step2: Solve for \(x\)

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

Answer:

\(18.84\)