# 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 from the mouse hole did he place the cheese?

### Example 7

A tilted tree stands at a height of 30.6 feet, measured straight from its topmost point to the ground. If the tree is actually 32.9 feet tall along its trunk, what angle does the tree make with the ground?