Question

find the measure of x.
round to the nearest hundredth.

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 42^{\circ}\), the opposite side is \(17\), and the adjacent side is \(x\). So, \(\tan42^{\circ}=\frac{17}{x}\).

Step2: Solve for \(x\)

Rearrange the formula: \(x=\frac{17}{\tan42^{\circ}}\).
We know that \(\tan42^{\circ}\approx0.9004\). Then \(x = \frac{17}{0.9004}\).
Calculate \(\frac{17}{0.9004}\approx18.88\).

Answer:

\(18.88\)