Question

6 multiple choice 1 point find the value of the variables. if your answer is not an integer, leave it in simplest radical form. not drawn to scale $x = 19sqrt{3}, y = 38$ $x = 38, y = 19sqrt{3}$ $x = 19, y = 38sqrt{3}$ $x = 38sqrt{3}, y = 19$

Explanation:

Step1: Use the property of a 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, the side opposite the 30° angle is half the hypotenuse. Let the side opposite 30° be \(a\), the side opposite 60° be \(a\sqrt{3}\), and the hypotenuse be \(2a\). Here, the side opposite 30° is \(19\), so the hypotenuse \(y = 2\times19=38\).

Step2: Find the other side

The side opposite 60° (let's call it \(x\)) is \(19\sqrt{3}\) (since if \(a = 19\), then the side opposite 60° is \(a\sqrt{3}\)).

Answer:

\(x = 19\sqrt{3},y = 38\) (the first option)