Question

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

Answer 1

Error in question:
If `b=11` and we are to solve for `color(red)(c)` then `color(green)(c=sqrt(146)~~12.08305)`
If `color(red)(c)=11` and we are to solve for `b` then `color(green)(b=4sqrt(6)~~9.797959)`

Explanation:

By Pythagorean Theorem (since `c` is the hypotenuse)
`color(white)("XXX")a^2+b^2=c^2`

If we are trying to find the value of `b`, then
`color(white)("XXX")b=sqrt(c^2-a^2)`

If we are trying to find the value of `c`, then
`color(white)("XXX")c=sqrt(a^2+b^2)`

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

Answer 2

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, " " rArr c = sqrt146`
`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, " " rArr b = sqrt96`
`b= 9.80 " " or4sqrt6`