Question

a) x = 20, y = 5√3
b) x = 10, y = 5√6/2
c) x = 5√3, y = 20
d) x = 10, y = 5√3

Explanation:

Step1: Use the properties of a \(30 - 60-90\) triangle

In a \(30 - 60 - 90\) triangle, if the side adjacent to the \(60^{\circ}\) angle (shorter leg) is \(a = 5\), the hypotenuse \(x\) (opposite the \(90^{\circ}\) angle) is related to the shorter leg by the formula \(x = 2a\).

$$x=2\times5 = 10$$

Step2: Find the longer leg \(y\)

The longer leg \(y\) (opposite the \(60^{\circ}\) angle) is related to the shorter leg \(a\) by the formula \(y=a\sqrt{3}\).

$$y = 5\sqrt{3}$$

Answer:

D. \(x = 10,y = 5\sqrt{3}\)