Question

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

Answer 1

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`