teh length of the hypotenuse of an isoscleles right triangle is 8 in. what is the length of one leg?

Question

how do you do this?

Answer 1

For an isosceles right triangle, the legs are the same - isosceles triangles have two sides that are the same. For an isosceles right triangle, this is also a 45-45-90 triangle (isosceles triangles have equal base angles).

In a 45-45-90 triangle, the sides are related through the ratio of 1:1:sqrt(2). So if the hypotenuse is 8, then we can find the legs by dividing by sqrt(2).

8/sqrt(2) = 8sqrt(2)/2 = 4sqrt(2)

If you didn't know the ratio, you can always use the Pythagorean theorem, c^2 = a^2 + b^2. a and b are going to be the same, since it's an isosceles triangle. So you'd have

c^2 = a^2 + b^2
c^2 = 2a^2
8^2 = 2a^2
64 = 2a^2
32 = a^2
a = 4sqrt(2)