# Using the Pythagorean theorem how would you find B if A =12 and c=17?

Aug 11, 2016

Depending on which side is the hypotenuse,

$b = \sqrt{145} , \mathmr{and} b = \sqrt{433}$

#### Explanation:

It is not clear from the question which side is the hypotenuse.
The sides are usually given as either AB or $c$ and not A or B which indicate points.

Let's consider both cases.

"If c is the hypotenuse"

${a}^{2} + {b}^{2} = {c}^{2} \text{ } \Rightarrow {b}^{2} = {c}^{2} - {a}^{2}$

${b}^{2} = {17}^{2} - {12}^{2}$

${b}^{2} = 145$

$b = \sqrt{145} = 12.04$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
If $c$ is NOT the hypotenuse.

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

${b}^{2} = {12}^{2} + {17}^{2}$

${b}^{2} = 433$

$b = \sqrt{433} = 20.81$