Question

Question #03d63

Answer 1

Use the Pythagorean Theorem (see below).

Explanation:

You may or may not have heard of the Pythagorean Theorem, which is used to find a missing side length of a right triangle from `2` previously known side lengths. Stated simply, the formula is:

We can use two side lengths to find the remaining one using this Pythagorean Theorem, `a^2 + b^2 =c^2`.

In case you don't know, a right triangle is a triangle with one angle measuring `90^@`.

Here is an example of how we can divide an isosceles triangle into two right triangles (using a line of symmetry):

Now, let's begin the problem. We are given the base and sides, and are asked to find the height. Using the Pythagorean Theorem and one of the two right triangles formed from dividing our isosceles triangle in half, we can assume that `a=40/2` (half of the base), and `c=29`. Our job is to find `b`:

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

`(20)^2 + b^2 = (29)^2`

`(400) + b^2 =841`

`b^2=441`

`b=sqrt(441)`

`b=color(blue)(21" inches"`

I hope that helps!