# In a 30-60-90 triangle, what is the length of the other leg and hypotenuse if the short leg is 5 in?

Jul 30, 2018

Other leg $= 5 \sqrt{3}$ in., hypotenuse $= 10$ in.

#### Explanation:

For a $30 - 60 - 90$ triangle, sides are in the ratio

$1 : \sqrt{3} : 2$ where 1 is the shorter side, $\sqrt{3}$ the other side and 2 the hypotenuse.

Given : short leg = 5 in.

$\therefore$ other leg $= \sqrt{3} \cdot 5 = 5 \sqrt{3}$ in.

Hypotenuse $= 2 \cdot 5 = 10$ in.