Right Triangle Applications

timer Asked: Sep 22nd, 2015

Question description

Apply your knowledge of basic right triangle trigonometry to solve real-world application problems. In each of the problems, you will use the basic trigonometric functions of sine, cosine, and/or tangent to solve problems involving right triangles.

Choose any four of the following five problems applying trigonometry to solve real-world application problems. For each problem:

  1. Sketch of the situation described. In your sketch, label each of the measurements given, as well as the unknown quantity. Each sketch should also indicate which angle measures 90 degrees.

  2. Apply the basic trigonometric functions of sine, cosine, and tangent to answer the question.

  3. Round all trigonometric function values to the nearest thousandth and round all final answers to the nearest whole number.

  4. Write at least one sentence to explain the meaning of the answer for the situation.

1. The shadow of a vertical tower is 50 m long when the angle of elevation of the sun is 35°. Find the height of the tower.

2. An airplane is flying 12,330 feet above level ground. The angle of depression from the plane to the base of a building is 11°. How far must the plane fly horizontally before it is directly over the building?

3. A 25-foot ladder is leaning against a building so that it makes an angle of 65° with the ground. How far up the building will the ladder reach?

4. From a window 20 feet above the ground, the angle of elevation to the top of a building across the street is 78°, and the angle of depression to the base of the same building is 15°. Find the height of the building across the street.

5. A person standing 100 feet from the base of the tree looks up to the top of the tree with an angle of elevation of 52°. Assuming that the person’s eyes are 5 feet above the ground, how tall is the tree?

Part II: Create Your Own Problem

6. Now create your own, original problem in which you use the basic right triangle trigonometric functions of sine, cosine, and/or tangent to solve the problem.

  1. In two to three sentences, write a description of the problem, including known and unknown measurements. Your problem should describe a real-world situation such as those in the previous section.

  2. Draw a picture of the problem, labeling all known and unknown quantities, as well as the location of the right angle.

  3. Solve the problem showing all necessary steps and work.

  4. Write a sentence to explain the meaning of the answer for your problem.

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