# Given right triangle ABC, with right angle at C, if a = 5 and b = 11 use the pythagorean theorem to solve for b?

Jun 12, 2016

Error in question:
If $b = 11$ and we are to solve for $\textcolor{red}{c}$ then $\textcolor{g r e e n}{c = \sqrt{146} \approx 12.08305}$
If $\textcolor{red}{c} = 11$ and we are to solve for $b$ then $\textcolor{g r e e n}{b = 4 \sqrt{6} \approx 9.797959}$

#### Explanation:

By Pythagorean Theorem (since $c$ is the hypotenuse)
$\textcolor{w h i t e}{\text{XXX}} {a}^{2} + {b}^{2} = {c}^{2}$

If we are trying to find the value of $b$, then
$\textcolor{w h i t e}{\text{XXX}} b = \sqrt{{c}^{2} - {a}^{2}}$

If we are trying to find the value of $c$, then
$\textcolor{w h i t e}{\text{XXX}} c = \sqrt{{a}^{2} + {b}^{2}}$

Simply insert whichever values were intended and perform (or have your calculator perform) the arithmetic.

Jun 12, 2016

The question needs to be clarified... b appears twice.
Either:$c = 12.08$ or b= 9.80 " or4sqrt6

#### Explanation:

The small letters represent the sides opposite the vertices with the same capital letter.
c would therefore be the hypotenuse.

This would involved squaring and adding the given sides.

${c}^{2} = {5}^{2} + {11}^{2} = 25 + 121$
If ${c}^{2} = 146 , \text{ } \Rightarrow c = \sqrt{146}$
$c = 12.08$

However, if b=11 is meant to be c = 11, it means we are trying to find one of the shorter sides (b), which would involve subtracting:

${b}^{2} = {11}^{2} - {5}^{2} = 121 - 25$
if ${b}^{2} = 96 , \text{ } \Rightarrow b = \sqrt{96}$
$b = 9.80 \text{ } \mathmr{and} 4 \sqrt{6}$