Question

find x and y using special right triangles. write your answer in simplified radical form.

Explanation:

Step1: Use the property of 30 - 60 - 90 triangle (hypotenuse)

In a 30 - 60 - 90 triangle, the side opposite the 30° angle is half the hypotenuse. Let the side opposite 30° be \(a = 9\), hypotenuse \(x\). Then \(a=\frac{1}{2}x\), so \(x = 2\times9=18\).

Step2: Use the property of 30 - 60 - 90 triangle (longer leg)

The longer leg \(y\) (opposite 60°) in a 30 - 60 - 90 triangle is \(y = a\sqrt{3}\). Since \(a = 9\), then \(y=9\sqrt{3}\).

Answer:

\(x = 18\), \(y = 9\sqrt{3}\)