Question

find z.
triangle with 10 in, 30°, 60°, right angle, z
write your answer in simplest radical form.
blank inches

Explanation:

Step1: Identify the triangle type

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

Step2: Determine the sides

The hypotenuse is 10 in. The side \(z\) is opposite the 60° angle. The side opposite 30° (let's call it \(x\)) is half the hypotenuse, so \(x = \frac{10}{2}=5\) in. Then the side opposite 60° (which is \(z\)) is \(x\sqrt{3}\), so \(z = 5\sqrt{3}\) in.

Answer:

\(5\sqrt{3}\)