Question

In the diagram, what is AC?

Answer 1

Hello! To solve this, we will be using Pythagorean Theorem multiple times in order to find AC.
The formula that we will be using is c=sqrt(a^2+b^2) (A and B both being the legs and C being the hypotenuse of the triangle.)

First we need to figure out the measurement of AD, and we know that AB (which AD lies within) is 21, but that's the measurement for the entire leg, what is it for the separate triangles? Well, we'll use the measurements from the right-side triangle to find what B is (you switch up the formula and turn it into b=sqrt(c^2-a^2) )

The measurement of our hypotenuse is 17 (CB) and our leg for A is 8 (CD), so by plugging these measurements in, we see that our other leg is 15.

Now we're almost done. We subtract 15 from 21 (21 - 15) to get what the left-side triangle equals and we get 6. And since CD is shared by both triangles, we use the original formula to solve for the hypotenuse.

When you plug everything in, you'll see that the answer is 10.

AC is 10