Question

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

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 25^{\circ}\), the opposite side is \(7\), and the adjacent side is \(x\). So, \(\tan(25^{\circ})=\frac{7}{x}\).

Step2: Solve for \(x\)

Rearrange the equation \(x=\frac{7}{\tan(25^{\circ})}\). We know that \(\tan(25^{\circ})\approx0.4663\). Then \(x = \frac{7}{0.4663}\).

Step3: Calculate the value

\(x=\frac{7}{0.4663}\approx15.01\)

Answer:

\(15.01\)