Question

solve for x.
x = ? ft
round to the nearest hundredth

Explanation:

Step1: Identify the trigonometric ratio

We have a right triangle with an angle of \(39^\circ\), the opposite side to the angle is \(5\) ft, and the adjacent side is \(x\). So we use the tangent function, which is \(\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}\).
\(\tan(39^\circ)=\frac{5}{x}\)

Step2: Solve for \(x\)

Rearrange the formula to solve for \(x\): \(x = \frac{5}{\tan(39^\circ)}\)
Calculate \(\tan(39^\circ)\approx0.8098\)
Then \(x=\frac{5}{0.8098}\approx6.17\)

Answer:

\(6.17\)