Question

11 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 = 16√3, y = 32
x = 32√3, y = 16
x = 32, y = 16√3
x = 16, y = 32√3

Explanation:

Step1: Use trigonometric ratios

In a right - triangle, if the angle is \(30^{\circ}\), and the side opposite to \(30^{\circ}\) is \(16\).
We know that \(\sin30^{\circ}=\frac{\text{opposite}}{\text{hypotenuse}}\), so \(\sin30^{\circ}=\frac{16}{y}\).
Since \(\sin30^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{16}{y}\), then \(y = 32\).

Step2: Use another trigonometric ratio

We also know that \(\tan30^{\circ}=\frac{\text{opposite}}{\text{adjacent}}\), so \(\tan30^{\circ}=\frac{16}{x}\).
Since \(\tan30^{\circ}=\frac{1}{\sqrt{3}}\), we have \(\frac{1}{\sqrt{3}}=\frac{16}{x}\), then \(x = 16\sqrt{3}\).

Answer:

\(x = 16\sqrt{3},y = 32\)