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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?