Question

9 multiple choice 1 point
find the value of the variable(s). if your answer is not an integer, leave it in simplest radical form.
not drawn to scale
$x = 40sqrt{3}, y = 20$
$x = 20, y = 40sqrt{3}$
$x = 20sqrt{3}, y = 40$
$x = 40, y = 20sqrt{3}$

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 \(a\), the side opposite the 60° angle is \(a\sqrt{3}\), and the hypotenuse is \(2a\). Here, the side opposite the 30° angle is \(20\) (the side opposite the 30° angle is the shorter leg).

Step2: Find the hypotenuse \(y\)

Since the hypotenuse \(y = 2a\) and \(a = 20\) (the side opposite 30°), then \(y=2\times20 = 40\).

Step3: Find the side \(x\) (opposite 60°)

Since the side opposite 60° is \(a\sqrt{3}\) and \(a = 20\), then \(x = 20\sqrt{3}\).

Answer:

\(x = 20\sqrt{3},y = 40\) (the third option)