Question

find p.
3√3 mi
60°
p
30°
write your answer in simplest radical form.
miles

Explanation:

Step1: Recall the properties of a 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, if the side opposite the 30° angle is \(x\), the side opposite the 60° angle is \(x\sqrt{3}\), and the side opposite the 90° angle is \(2x\).
Let the side opposite the 30° angle be \(a\), the side opposite the 60° angle be \(b = 3\sqrt{3}\) mi, and the side opposite the 90° angle be \(p\).
Since \(b=x\sqrt{3}\) (where \(x\) is the side opposite the 30° angle), and \(b = 3\sqrt{3}\), then \(x\sqrt{3}=3\sqrt{3}\), so \(x = 3\) mi.

Step2: Use the ratio for the hypotenuse

The hypotenuse \(p\) (side opposite the 90° angle) in a 30 - 60 - 90 triangle is \(2x\).
Since \(x = 3\) mi, then \(p=2x\).

Answer:

\(6\) miles