# If a=5 and c=9, how do you find b?

Oct 8, 2015

Assuming you are speaking of the lengths of the sides of a right-angled triangle:

$b = \sqrt{{c}^{2} - {a}^{2}} = \sqrt{81 - 25} = \sqrt{56} = 2 \sqrt{14}$

#### Explanation:

Pythagoras theorem tells us: ${a}^{2} + {b}^{2} = {c}^{2}$

Subtract ${a}^{2}$ from both sides to get:

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

Then take the (positive) square root of both sides to get:

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

In our case, $a = 5$ and $c = 9$, so...

$b = \sqrt{{9}^{2} - {5}^{2}} = \sqrt{81 - 25} = \sqrt{56}$

$= \sqrt{{2}^{2} \cdot 14} = \sqrt{{2}^{2}} \cdot \sqrt{14} = 2 \sqrt{14}$

$\approx 7.4833$