Question

the shorter leg of a 30°-60°-90° triangle has a length of $7\sqrt{2}$ feet. what is the length of the hypotenuse?
write your answer in simplest radical form.
\boxed{} feet

Explanation:

Step1: Recall 30-60-90 triangle ratios

In a \(30^\circ\)-\(60^\circ\)-\(90^\circ\) triangle, the ratios of the sides are \(1 : \sqrt{3} : 2\), 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: Identify the shorter leg value

Here, the shorter leg \(x = 7\sqrt{2}\).

Step3: Calculate the hypotenuse

Using the hypotenuse formula \(2x\), substitute \(x = 7\sqrt{2}\):
\(2\times7\sqrt{2}=14\sqrt{2}\)

Answer:

\(14\sqrt{2}\)