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

Answer:

Each leg = $x=4\sqrt{2}$

Step-by-step 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:

$x^2 + x^2 = 8^2\\2x^2=64\\x^2=32\\x=\sqrt{32}$

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

1. $\sqrt{xy} =\sqrt{x} \sqrt{y}$
2. $\sqrt{x} \sqrt{x} =x$

Now, lets solve for x:

$x=\sqrt{32}\\ x=\sqrt{2} \sqrt{2} \sqrt{2} \sqrt{2} \sqrt{2} \\x=(2)(2)\sqrt{2} \\x=4\sqrt{2}$

This is the exact answer. Each leg length.