At a Glance - 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 the Tootsie-Pop, the delicious creamy filling in the center of every éclair.

Bon appétit, because it's time for trigo-nom-nom-nom-etry!

Trigonometry is a fancy term for triangle measurement. More specifically, it relates the angle measurements of triangles to the lengths of their sides. It's a big scary word, but the actual concepts aren't too complicated as long as you keep in mind everything we've talked about so far.

Example 1

 Find the value of x.

Example 2

 What is the measurement of ∠D if tan D = 1?

Example 3

 Find the measure of ∠H in ∆GHI when the triangle has the following points: G (0, -5), H (-5, -5), I (0, 2).

Example 4

 What's the measure of ∠KMN?

Exercise 1

Express sin P, cos P, and tan P using a, b, and c.

Exercise 2

What are the three angles of a right triangle with side lengths of 15, 36, and 39?

Exercise 3

What is the length of a right triangle's hypotenuse if the side adjacent to a 78° angle is 1?

Exercise 4

Find the value of x and y.

Exercise 5

Find the value of x.

Exercise 6

Find the value of x and y.

Exercise 7

Find all the angles of a triangle with points X (-4, 6), Y (-4, -2), and Z (3, -2).

Exercise 8

Alex is a tightrope walker. He wants to tie a 40-foot rope to two poles so that he can practice for his upcoming circus show. After all, practice makes perfect. The poles are arranged in this way.

To which two poles should he tie his rope if he wants to walk across greatest distance possible?