# The shorter leg of a 30°- 60°- 90° right triangle is 7.5 inches. How long is the longer leg and the hypotenuse?

Jun 8, 2015

The longer leg is $7.5 \sqrt{3}$ inches.
The hypotenuse is $15.0$ inches.

#### Explanation:

A right triangle with angles ${30}^{\circ} - {60}^{\circ} - {90}^{\circ}$ is one of the standard trigonometric triangles with sides in the ratio:
$\textcolor{w h i t e}{\text{XXXX}}$$1 : \sqrt{3} : 2$

If the shortest side is 7.5 inches,
the other two sides are
$\textcolor{w h i t e}{\text{XXXX}}$$7.5 \sqrt{3} \mathmr{and} 15.0$ inches.