How do you do #18 in Test 6 Section 3 without a calculator?

The key to this one is recognizing that you’ve got similar triangles. First, both triangle *CDB* and triangle *CEA* contain angle *C*. The question also tells you that , which means that angle *CDB* is also a right angle. Therefore, you have angle-angle similarity.

It’s also good to recognize a 6-8-10 triangle quickly. Know your Pythagorean triples! 🙂

From there, all you need to do is recognize that the length of is 3 times the length of , which means all the sides of triangle *CEA* are 3 times the length of their corresponding sides in triangle *CDB*. Therefore, because the length of is 10, the length of must be 30.