Question

find p.
write your answer in simplest radical form.
kilometers
submit
work it out
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Explanation:

Step1: Identify trigonometric ratio

We use tangent for the 30° angle: $\tan(\theta) = \frac{\text{opposite}}{\text{adjacent}}$
Here, $\theta=30^\circ$, opposite side = $p$, adjacent side = $9$ km.
Expression: $\tan(30^\circ) = \frac{p}{9}$

Step2: Substitute $\tan(30^\circ)$ value

$\tan(30^\circ) = \frac{1}{\sqrt{3}}$
Expression: $\frac{1}{\sqrt{3}} = \frac{p}{9}$

Step3: Solve for $p$

Multiply both sides by 9, rationalize the denominator.
Expression: $p = \frac{9}{\sqrt{3}} = 3\sqrt{3}$

Answer:

$3\sqrt{3}$ kilometers