Question

(help)

use 2-3 sentences to explain, in your own words, how you find the value of the hypotenuse when given
a leg in a 45-45-90 triangle. explain using the following vocabulary words: right triangle, isosceles
triangle, leg, hypotenuse, and square root.

Answer 1

Let the length of the leg be
`x`. Since the right triangle is isosceles, the length of each leg is
`x`, and thus, by the Pythagorean theorem, the hypotenuse has a length equal to the square root of the sum of the squares of the lengths of the legs, or
`√(x^2+x^2)=x√(2)`.

Using this result, we see that to find the length of the hypotenuse, we multiply the length of the leg by
`√(2)`.