# How do you find the length of the missing side of a right triangle if the hypotenuse is 4sqrt3 and the short side is 2?

Jun 11, 2015

I found the length as $6.6$

#### Explanation:

I would use Pythagora's Theorem as:
${c}^{2} = {a}^{2} + {b}^{2}$
where $c = 4 \sqrt{3}$ is the hipotenuse.
So:
$16 \cdot 3 = 4 + {b}^{2}$
$b = \sqrt{48 - 4} = 6.6$

Jun 11, 2015

The length of the missing side is exactly $2 \sqrt{11}$.

#### Explanation:

Use the Pythagorean theorem ${c}^{2} = {a}^{2} + {b}^{2}$, where $c$ is the hypotenuse of a right triangle, and $a$ and $b$ are sides or legs of the right triangle.

For this question:

$c = 4 \sqrt{3}$
$a = 2$
b=?

Solve the Pythagorean theorem for $a$.

${b}^{2} = {c}^{2} - {a}^{2}$

${b}^{2} = {\left(4 \sqrt{3}\right)}^{2} - {2}^{2}$ =

${b}^{2} = 16 \left(3\right) - 4$ =

${b}^{2} = 48 - 4 = 44$

$b = \sqrt{44}$ =

$b = \sqrt{4 \times 11}$ =

$b = 2 \sqrt{11}$