To review these concepts, go to Law of Sines and Cosines Help
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.
Ask a Question
Have questions about this article or topic? AskPopular Articles
 Kindergarten Sight Words List
 First Grade Sight Words List
 10 Fun Activities for Children with Autism
 Grammar Lesson: Complete and Simple Predicates
 Definitions of Social Studies
 Child Development Theories
 Signs Your Child Might Have Asperger's Syndrome
 Social Cognitive Theory
 How to Practice Preschool Letter and Name Writing
 Theories of Learning