Question

Use the Pythagorean Theorem to find the length of the leg in the triangle shown below. The figure shows a right triangle with one leg marked 20. The hypotenuse is marked 52.

Answer 1

48

Explanation:

The Pythagorean Theorem is:

`a^2+b^2=c^2`

where
`a` and
`b` are the legs of the right triangle.
`c` is the hypotenuse of the triangle.

In this right triangle, we know that one leg is 20 and the hypotenuse is 52. Therefore,

`a=20`

`c=52`

Since we don't know the other leg, we can leave it as
`b`. Substitute the values into the theorem.

`20^2+b^2=52^2`

Evaluate the exponents first.

⇒ 20²=20*20=400

⇒ 52²= 52*52= 2704

`400+b^2=2704`

Since we want to find
`b`, we must isolate
`b`. First, subtract 400 from both sides of the equation.

`400-400+b^2=2704-400`

`b^2=2704-400`

`b^2=2304`

`b` is being squared. The inverse of a square is a square root. Take the square root of both sides of the equation.

`√(b^2)=√(2304)`

`b=√(2304)`

`b=48`

The length of the other leg is 48