Study Guide

# Right Triangles and Trigonometry

## Right Triangles and Trigonometry Introduction

Your mom has been telling you for the past three months that she doesn't want anything for her birthday. "Just make me something," she says. "It'll mean more to me if it's from the heart." Of course, you know that the only reason she says that is because she knows you can't afford that new massaging spa chair from Brookstone that she's had her eye on.

So you decide to build her a bookcase. Why not? She likes books. And you've certainly gotten tired of tripping over her Danielle Steel novels every time you walk up and down the stairs. Seems like a win-win.

But once you sit down with your carpenter pants and toolbox, you realize that it's not just going to be about taking pre-cut boards and slapping them together with Krazy Glue. You're going to have to cut some of these puppies, fit them into grooves, and compute angles and dimensions and stuff. In other words, you'd better get pretty cozy with geometry or this bookcase is going to look like a set piece from a Tim Burton movie.

We know that geometry can be tougher and drier than your grandma's homemade brisket. Sometimes it seems like all these shapes and proofs and theorems have joined forces to make your life an endless swirling vortex of headaches and anxiety. We know the feeling.

News flash. It doesn't have to be that way. All we have to do is look at geometry from the right…tri-angle. Good one, eh?

We know a right triangle is the opposite of a left triangle, but why does its 90° angle matter so much? Britney Spears really wants us to give her a sign (and then hit her, baby, one more time), but could she have meant "sine" instead? If Law & Order wants to have as many spinoffs as possible, why isn't "Law of Cosines" one of them? We'll answer these questions and many more.

In this unit, we'll get up-close and personal with right triangles, so keep some Tic Tacs handy. Mr. Pythagoras, a gentlemanly fellow, will enlighten us about his theorem, but don't buy into the hype-otenuse. We'll venture straight into the delicious world of trigo-nom-nom-nom-etry and as long as we prove ourselves (and a few other things, like proofs), that bookcase will be done and looking fabulous in no time. Eat your heart out, Brookstone.

## Right Triangles and Trigonometry Resources

### Websites

Euclid's Elements: Book One
This all-inclusive site covers everything geometry, split up into bite-sized pieces. Books One and Two have solid information and a quick search for "triangle" will get you what you need to know.

Dave's Short Trig Course
This is a comprehensive and straightforward website dedicated to trigonometry exclusively. It's separated into short sections, but it covers a lot of valuable information in a good, approachable way.

1000 Ways to Prove the Pythagorean Theorem
If you can't get enough of proofs or Pythagoras, then you might be interested in the many, many, many different ways you can prove the Pythagorean Theorem. Pick your favorite and share it on Facebook!

The Ultimate Pythagorean Theorem Test
Answer these nine challenging questions using the Pythagorean Theorem, discover the password, and win the treasure. Have you got what it takes?

### Videos

eHow: Geometry & Trigonometry
A series of videos explaining the most important elements of geometry and trigonometry as well as how they're applicable in everyday life. Ever considered a career in geometry or trigonometry? These PhD's have got your back.

NeoK12: Trigonometry
Educational videos explaining trigonometry and its slightly more complicated side, including graphs, radians, and trigonometric identities. These snippets can give you a good feel for what trigonometry is all about, and help supplement all the stuff you already know.

### Games and Tools

Geometry Calculators and Solvers
This little doodad can be useful in checking your work. It'll solve any triangle for us, and all we have to do is input the information we know already. It applies the same theorems and laws we learned, but it's way faster.

Pythagorean Theorem Jeopardy
Enter your name and start playing Jeopardy, Pythagorean Theorem-style. This is a great way to make use of the Pythagorean Theorem for those who have a little trouble with it or just want the extra practice.

Trigonometry Escape
Play this neat game and use a bunch of items, logic, and trigonometry to escape from a room. It's tangentially related, but still a whole lot of thought-provoking and sometimes frustrating fun.