Find the measurements of all angles in the triangle.
Hint
Use the Law of Cosines at least once to start. After that, free reign.
Answer
34.8°, 58.8°, 86.4°
Example 2
Solve the triangle.
Hint
We'll have memorized the Law of Cosines by the end of this chapter.
Answer
a ≈ 529.2; b = 600; c = 200; A = 60°; B = 100.9°; C = 19.1°
Example 3
Find ∠R if ∆QRS has the following points: Q (3, 1), R (-1, 4), and S (1, -2).
Hint
Use the distance formula: . Finding the distances is the same as finding the side lengths.
Answer
R ≈ 34.7°
Example 4
Find the value of x.
Hint
Use the Law of Cosines. Now use it again.
Answer
x ≈ 88.3
Example 5
Find the length of AD if ∠BCE = 180° exactly.
Hint
We can use the Law of Cosines to find the lengths of AC and CD. Once we know the measure of ∠ACD, finding the length of AD should be easy.
Answer
AD ≈ 39.3
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?
Hint
Tom makes a known angle between two known side lengths of a triangle.
Answer
Tom placed the cheese about 10.4 feet away from Jerry's mouse hole.
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?
Hint
The Pythagorean Theorem will come in handy to calculate the last side of the triangle, since that height of 30.6 makes a right angle with the ground. Once all the sides are known, we can find the angle we want.
Answer
The tree makes an angle of approximately 68.5° with the ground.
. Finding the distances is the same as finding the side lengths.
