Question

In the right triangle shown, AC=BC and AB=8

How long are each of the legs?
Answer exactly, using a radical if needed​

Answer 1

Each leg =
`x=4√(2)`

Explanation:

Angle C is the right angle, so the side oppsoite of the right angle is the "HYPOTENUSE", which is 8.

THe legs are AC and BC, which are x each.

Using pythagorean theorem, we can solve for x (length of each leg).

Pythagorean theorem = Leg^2 + Leg^2 = Hypotenuse^2

So we can write:

`x^2 + x^2 = 8^2`

Simplifying and solving for x:

`x^2 + x^2 = 8^2\\2x^2=64\\x^2=32\\x=√(32)`

We need to keep an exact answer (with radicals), so we need to simplify this using the two rules of radicals below:

1. 
   `√(xy) =√(x) √(y)`
2. 
   `√(x) √(x) =x`

Now, lets solve for x:

`x=√(32)\\ x=√(2) √(2) √(2) √(2) √(2) \\x=(2)(2)√(2) \\x=4√(2)`

This is the exact answer. Each leg length.