In a right triangle, if #a=3# and #b=6#, what is the value of #c#?

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Answer 1 · 2016-02-10T13:01:50

#c=sqrt(45)#

When trying to find the area of a right triangle, we use the Pythagorean Theorem:

#color(red)a^2+color(blue)b^2=color(green)c^2#

In this case we are given the values for #color(red)a# and #color(blue)b#, so:

#(color(red)(3))^2+(color(blue)6)^2=color(green)c^2#

Which is equal to:

#(color(red)(9))+(color(blue)36)=color(green)c^2#
#color(purple)45=color(green)c^2#
#sqrt(color(purple)45)=sqrt(color(green)c^2)#

So:

#color(green)c=color(green)(sqrt(45)=3sqrt(5))#

Note: The answer could also be a decimal or fraction. I chose to represent it in this way because it is the most exact. You could find either of the other answers by using a calculator.