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Law of Sines and Cosines Practice Problems

By — McGraw-Hill Professional
Updated on Oct 4, 2011

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.

  1. cos −1 (cos π /8)
  2. tan(tan −1 −1)
  3. cos −1 1/2
  4. sin −1 1/2
  5. tan −1 0
  6. sin −1 0.9
  7. Solve the triangle.

Trigonometry Practice

Fig. 13.59.

  1. A 20-foot 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?

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

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

  4. 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

  1. π /8 radians
  2.  −1 radians
  3. π /3 radians
  4. π /6 radians
  5. 0 radians
  6. Approximately 1.1 radians

Trigonometry Solutions

  1.  

     

    Trigonometry Solutions

    Fig. 13.60

    Trigonometry Solutions

  2. We will use the Law of Sines twice.

    Trigonometry Solutions

     

    Trigonometry Solutions

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

    Trigonometry Solutions

  4.  

     

    Trigonometry Solutions

    Fig. 13.61

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

    Trigonometry Solutions

    The plane is about 8485 feet from the blue car and about 7536 feet from the white car.

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