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Law of Sines and Cosines Practice Problems
Practice
When rounding is necessary, please give your solutions accurate to one decimal place. The angles for Problems 1–6 are in radians.
 cos ^{−1} (cos π /8)
 tan(tan ^{−1} −1)
 cos ^{−1} 1/2
 sin ^{−1} 1/2
 tan ^{−1} 0
 sin ^{−1} 0.9
 Solve the triangle.

A 20foot ladder is leaning against a wall. The base of the ladder is four feet from the wall. What angle is formed by the ground and the ladder?

Solve the triangle: A = 42°, a = 11, and b = 6.

Find all three angles for the triangle whose sides are 6, 8, and 10.

A plane is flying over a highway at an altitude of 6000 feet. A blue car is traveling on a highway in front of the plane and a white car is on the highway behind the plane. The angle of elevation from the blue car to the plane is 45°. If the cars are two miles apart, how far is the plane from each car? (Hint: Consider the triangle formed by the cars and plane as two right triangles that share a leg.)
Solutions
 π /8 radians
 −1 radians
 π /3 radians
 π /6 radians
 0 radians
 Approximately 1.1 radians


We will use the Law of Sines twice.

Let a = 6, b = 8, and c = 10. We will first use the Law of Cosines to find A . Then we will use the Law of Sines to find B .

Let b represent the side of the original triangle that is opposite the angle 45°. Let w represent the side opposite W , which is also the distance from the plane to the blue car. Two miles is 2(5280) = 10,560 feet.
The plane is about 8485 feet from the blue car and about 7536 feet from the white car.
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