Question

How do you find the area of the triangle when 24ft tall and the hypotenuse is 26ft?

Answer 1

The area would be `120 ft^2`

Explanation:

Pythagorean Theorem says this for triangle side lengths:

`a^2 + b^2 = c^2`
c being the hypotenuse and a/b being the leg lengths

Therefore, we can plug in 26 for c, 24 for a, and solve for b, which will be the base.

`24^2 + b^2 = 26^2`
`576 + b^2 = 676`
`b^2 = 100`
`b = 10`

Now that we know the base length, and the height, we can use the area for a triangle:

`1/2bh = A`

Let's plug in the remaining variables and solve for the answer.

`1/2(10)(24) = A`
`240/2 = A`
`120 = A`

Put your units on (`ft^2`) and you get the answer at `120 ft^2`
Hope this helped!