Question

What is the length of the leg of a 45°-45°-90° triangle with a hypotenuse length of 11?

Answer 1

7.7782 units

Explanation:

Since this is a `45^o-45^o-90^o` triangle, we can determine two things first of all.
1. This is a right triangle
2. This is an isosceles triangle

One of the theorems of geometry, the Isosceles Right Triangle Theorem, says that the hypotenuse is `sqrt2` times the length of a leg.

`h = xsqrt2`
We already know the length of the hypotenuse is `11` so we can plug that into the equation.
`11=xsqrt2`
`11/sqrt2=x` (divided `sqrt2` on both sides)
`11/1.4142=x` (found an approximate value of `sqrt2`)
`7.7782=x`

Answer 2

Each leg is `7.778` units long

Explanation:

Knowing that two angles are equal to `45°` and that the third is a right angle, means that we have a right-angled isosceles triangle.

Let the length of the two equal sides be `x`.

Using Pythagoras's Theorem we can write an equation:

`x^2 +x^2 =11^2`

`2x^2 = 121`

`x^2 = 121/2`

`x^2 = 60.5`

`x = +-sqrt(60.5)`

`x = +7.778" "or" " x= -7.778`

However, as sides cannot have a negative length, reject the negative option.