Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 38^{\circ}\), the opposite side to \(\angle T\) is \(RS = 99\), and the hypotenuse is \(RT=x\). So, \(\sin(38^{\circ})=\frac{99}{x}\).

Step2: Solve for \(x\)

Rearrange the equation \(\sin(38^{\circ})=\frac{99}{x}\) to get \(x=\frac{99}{\sin(38^{\circ})}\).
We know that \(\sin(38^{\circ})\approx0.6157\). Then \(x=\frac{99}{0.6157}\approx160.8\).

Answer:

\(x\approx160.8\)