# Right Triangles and Trigonometry

### Example 1

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

### Example 2

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

### Example 3

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

### Example 4

Find the value of *x* and *y*.

### Example 5

Find the value of *x*.

### Example 6

Find the value of *x* and *y*.

### Example 7

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

### Example 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?