# Topics Exercises

#### Geometric Mean

To find altitudes of unruly triangles, we can just use the geometric mean, which actually isn't mean at all. It's quite nice. Just multiply two numbers together and take the square root. The...

#### The Pythagorean Theorem

Sure, we could cut triangles in two until the cows come home, but there's an even simpler way to calculate the sides of a right triangle.Mr. Pythagoras has once again come back to haunt us, doing w...

#### Special Right Triangles

Right triangles are special by themselves, but there are two magical types of right triangles that we think deserve mentioning: 45-45-90 triangles and 30-60-90 triangles. No, those aren't their...

#### Trigonometry

We've learned about the Pythagorean theorem, the geometric mean, and magical right triangles that would give Harry Potter a run for his money. In this chapter, we've finally reached the center of t...

#### Law of Sines

The Law of Sines can be used to find the angles and side lengths of triangles that aren't right triangles. It has little to do with crop circles, aliens, or Mel Gibson.The triangle above rep...

#### Law of Cosines

The Law of Sines can be very useful, but there are cases where it won't do. Don't get us wrong. It's taken us this far and we owe it some gratitude. But no man is an island and the Law of Si...