Question

find p.
17√3 yd
60°
30°
p
write your answer in simplest radical form.
yards

Explanation:

Step1: Identify trigonometric ratio

We use cosine for the 30° angle: $\cos(30^\circ) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{17\sqrt{3}}{p}$

Step2: Solve for $p$

Rearrange to isolate $p$: $p = \frac{17\sqrt{3}}{\cos(30^\circ)}$
Substitute $\cos(30^\circ) = \frac{\sqrt{3}}{2}$:
$p = \frac{17\sqrt{3}}{\frac{\sqrt{3}}{2}} = 17\sqrt{3} \times \frac{2}{\sqrt{3}}$

Step3: Simplify the expression

Cancel $\sqrt{3}$ terms: $p = 17 \times 2$

Answer:

34 yards