# Charlene is trying to find the unknown sides of a right triangle with a 30° acute angle, whose hypotenuse measures 12sqrt2. What is Charlene's error?

Jan 8, 2018

Unknown sides are $6 \sqrt{2} , 6 \sqrt{6}$

#### Explanation:

Three angles of the right triangle are

$A = {30}^{0} , B = {60}^{0} , C = {90}^{0}$

Sides will be in the ratio,
$x : x \sqrt{3} : 2 x$ as May be seen from the diagram above.

Given hypotenuse $12 \sqrt{2} = 2 x$

$x = \frac{12 \sqrt{2}}{2} = 6 \sqrt{2}$

Side opposite to ${30}^{0} = x = 6 \sqrt{2}$

Side opposite to ${60}^{0} = x \sqrt{3} = 6 \sqrt{2} \cdot \sqrt{3} = 6 \sqrt{6}$