Question

find the lengths of x and y.
5
60°
30°
x
o x = 6; y = 8
o x = 6; y = 9
o x = 5√2; y = 10
o x = 5√3; y = 10

Explanation:

Step1: Use the property of a \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle for the hypotenuse \(y\)

In a \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle, the side opposite the \(30^{\circ}\) angle is half the hypotenuse. The side opposite \(30^{\circ}\) is \(5\). So, \(y = 2\times5=10\).

Step2: Use the Pythagorean theorem or the property of \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle for \(x\)

In a \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle, the side opposite \(60^{\circ}\) is \(\sqrt{3}\) times the side opposite \(30^{\circ}\). The side opposite \(30^{\circ}\) is \(5\), so \(x = 5\sqrt{3}\).

Answer:

\(x = 5\sqrt{3}; y = 10\) (the fourth option)