Question

solve for ( x ). round to the nearest tenth, if necessary.
(image of a right triangle ( nop ) with right angle at ( o ), ( angle p = 69^circ ), ( op = 80 ), ( no = x ))

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
Here, $\theta = 69^\circ$, opposite side to $\angle P$ is $x$, adjacent side is $80$.
So $\tan(69^\circ) = \frac{x}{80}$

Step2: Isolate $x$

Rearrange to solve for $x$:
$x = 80 \times \tan(69^\circ)$

Step3: Calculate value

Use $\tan(69^\circ) \approx 2.6051$
$x \approx 80 \times 2.6051 = 208.408$

Step4: Round to nearest tenth

$x \approx 208.4$

Answer:

$208.4$