Question

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

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 40^{\circ}\), the opposite side to \(\theta\) is \(EF = 9\), and the adjacent side is \(GF=x\). So, \(\tan40^{\circ}=\frac{9}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{9}{\tan40^{\circ}}\). Since \(\tan40^{\circ}\approx0.8391\), then \(x=\frac{9}{0.8391}\approx10.7\).

Answer:

\(x\approx10.7\)