Question

solve for x. round to the nearest tenth, if necessary.
answer attempt 1 out of 2
x =

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 58^{\circ}\), the opposite side \(= YT = 6.7\), and the adjacent side \(= YZ=x\). So, \(\tan(58^{\circ})=\frac{6.7}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to \(x=\frac{6.7}{\tan(58^{\circ})}\). Since \(\tan(58^{\circ})\approx1.600334529\), then \(x=\frac{6.7}{1.600334529}\approx4.2\).

Answer:

\(4.2\)