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.

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