Question

the shorter leg of a 30°-60°-90° triangle is 1 yard long. how long is its longer leg? write your answer in simplest radical form. yards

Explanation:

Step1: Recall 30-60-90 triangle ratios

In a \(30^\circ - 60^\circ - 90^\circ\) triangle, the sides are in the ratio \(1:\sqrt{3}:2\), where the shorter leg (opposite \(30^\circ\)) is \(x\), the longer leg (opposite \(60^\circ\)) is \(x\sqrt{3}\), and the hypotenuse is \(2x\).

Step2: Apply the ratio to given shorter leg

Given the shorter leg \(x = 1\) yard. The longer leg is \(x\sqrt{3}\). Substitute \(x = 1\) into the formula for the longer leg: \(1\times\sqrt{3}=\sqrt{3}\).

Answer:

\(\sqrt{3}\)