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