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

2 Answers
Alan P.
Jun 12, 2016

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.

EZ as pi
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, " " 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#

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