Question

20)
(right triangle with right angle, 60° angle, hypotenuse 16, legs x and y)
180 - 60 - 90 = 30

Explanation:

Step1: Identify the triangle type

This is a right - angled triangle with one angle \(60^{\circ}\), so it is a \(30 - 60-90\) triangle. In a \(30 - 60 - 90\) triangle, if the hypotenuse \(c = 16\), the side opposite the \(30^{\circ}\) angle (\(y\)) is given by \(y=\frac{c}{2}\).

$$y=\frac{16}{2}=8$$

Step2: Find the side \(x\)

The side opposite the \(60^{\circ}\) angle (\(x\)) is given by \(x = y\sqrt{3}\). Since \(y = 8\), then \(x=8\sqrt{3}\).

Answer:

\(x = 8\sqrt{3}\), \(y = 8\)