Question

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

Explanation:

Step1: Use sine function

In right - triangle \(OPQ\), \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here \(\theta = 23^{\circ}\), the opposite side to \(\theta\) is \(43\) and the hypotenuse is \(x\). So \(\sin(23^{\circ})=\frac{43}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{43}{\sin(23^{\circ})}\). Since \(\sin(23^{\circ})\approx0.3907\), then \(x = \frac{43}{0.3907}\approx110.1\).

Answer:

\(x\approx110.1\)