Question

find y. 60° 8 ft y 30° write your answer in simplest radical form. feet

Explanation:

Step1: Identify the triangle type

This is a \(30^{\circ}-60^{\circ}-90^{\circ}\) right - triangle. In a \(30^{\circ}-60^{\circ}-90^{\circ}\) triangle, the sides are in the ratio \(1:\sqrt{3}:2\). The side opposite the \(30^{\circ}\) angle is the shortest side, the side opposite the \(60^{\circ}\) angle is \(\sqrt{3}\) times the shortest side, and the hypotenuse is twice the shortest side.

Step2: Use the ratio

The hypotenuse is \(8\) ft. Let the side opposite \(30^{\circ}\) be \(x\), then \(2x = 8\), so \(x = 4\). The side \(y\) is opposite the \(60^{\circ}\) angle. Using the ratio, \(y=x\sqrt{3}\).

Step3: Calculate \(y\)

Since \(x = 4\), then \(y = 4\sqrt{3}\)

Answer:

\(4\sqrt{3}\)