How do you find the legs in a 45-45-90 triangle when its hypotenuse is 11?

1 Answer
Mar 23, 2018

The two legs of the right isosceles triangle are both #(11sqrt(2))/2 ~~7.78#.

Explanation:

Since two of the angles in this triangle are #45# degrees and it has a #90# degree angle, it is a right isosceles triangle. An isosceles triangle has two sides the same, which have to be the two legs in this triangle because a triangle can not have two hypotenuses.
According to the Pythagorean Theorem:
#a^2 + b^2 = c^2#
where #a# and #b# are the legs and #c# is the hypotenuse.
Since the two legs in this right triangle are the same, the formula can be altered to be:
#a^2 + a^2 = c^2#
#2a^2 = c^2#

Plugging in #10# for #c#:
#2a^2 = 11^2#
#2a^2 = 121#
#a^2 = 121/2#
#a = sqrt(121/2)#
#a = sqrt(121)/sqrt(2)#
#a = 11/sqrt(2)#
#a = (11sqrt(2))/2 ~~7.78#