# Right Triangles and Trigonometry

# Law of Cosines Exercises

### Example 1

Find the measurements of all angles in the triangle.

### Example 2

Solve the triangle.

### Example 3

Find ∠*R* if ∆*QRS* has the following points: *Q* (3, 1), *R* (-1, 4), and *S* (1, -2).

### Example 4

Find the value of *x*.

### Example 5

Find the length of *AD* if ∠*BCE* = 180° exactly.

### Example 6

In hopes to lure Jerry out and catch him, Tom has planted a piece of cheese at a distance away from his mouse hole. Tom is ready to pounce from his hiding spot, 7 feet away from the mouse hole and 10 feet away from the cheese. If the angle Tom makes is 73.1°, approximately how far away did he place the cheese?

### Example 7

A tilted tree stands at a height of 30.6 feet. The shadow it casts is 37.8 feet long, 12.1 feet past a perpendicular line from top of the tree to the ground. If the tree is actually 32.9 feet tall, what angle does the tree make with the ground?