Question

unit review - right triangles and trigonometry
solve for x.
39°
x
5 ft
x = ? ft
round to the nearest hundredth.

Explanation:

Step1: Identify trigonometric ratio

We use $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta=39^\circ$, opposite side $=5$, adjacent side $=x$.
$\tan(39^\circ)=\frac{5}{x}$

Step2: Rearrange to solve for x

Isolate $x$ by cross-multiplying.
$x=\frac{5}{\tan(39^\circ)}$

Step3: Calculate the value

Use a calculator to find $\tan(39^\circ)\approx0.8098$, then compute $x$.
$x\approx\frac{5}{0.8098}\approx6.17$

Answer:

$6.17$ ft