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, \(\theta = 12^{\circ}\), the opposite side is \(4\), and the adjacent side is \(x\). So, \(\tan(12^{\circ})=\frac{4}{x}\).

Step2: Solve for \(x\)

Rearrange the equation \(\tan(12^{\circ})=\frac{4}{x}\) to get \(x=\frac{4}{\tan(12^{\circ})}\).
We know that \(\tan(12^{\circ})\approx0.2126\). Then \(x = \frac{4}{0.2126}\).

Step3: Calculate the value of \(x\)

\(x=\frac{4}{0.2126}\approx18.81\)

Answer:

\(18.81\)