Question

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

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here, \(\theta = 32^{\circ}\), the opposite side is \(96\), and the hypotenuse is \(x\). So, \(\sin32^{\circ}=\frac{96}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{96}{\sin32^{\circ}}\). Since \(\sin32^{\circ}\approx0.5299\), then \(x=\frac{96}{0.5299}\approx181.2\).

Answer:

\(181.2\)