Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 58^{\circ}\), the opposite side to \(\theta\) is \(YT = 6.7\), and the adjacent side is \(YZ=x\). So, \(\tan58^{\circ}=\frac{YT}{YZ}\).

Step2: Substitute the values and solve for \(x\)

We know that \(\tan58^{\circ}\approx1.6003\). Substituting into the formula \(\tan58^{\circ}=\frac{6.7}{x}\), we can rewrite it as \(x=\frac{6.7}{\tan58^{\circ}}\).

$$x=\frac{6.7}{1.6003}$$

$$x\approx4.2$$

Answer:

\(x\approx4.2\)