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5.4 Applying Trigonometric Functions

5.4 Applying Trigonometric Functions. Application. Trig functions can be used to solve problems involving right angles. Example 1. If J=50 ° and j=12, find r. G. R. J. Example 2. The chair lift at a ski resort rises at an angle of 20.75 ° and attains a vertical height of 1200 ft.

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5.4 Applying Trigonometric Functions

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  1. 5.4 Applying Trigonometric Functions

  2. Application • Trig functions can be used to solve problems involving right angles.

  3. Example 1 • If J=50° and j=12, find r. G R J

  4. Example 2 • The chair lift at a ski resort rises at an angle of 20.75° and attains a vertical height of 1200 ft. • How far does the chair lift travel? • A film crew in a helicopter records an overhead view of a skier’s downhill run. How far away is the helicopter from the top of the mountain?

  5. TERMINOLOGY • Many word problems in trigonometry use the following definitions: • Angle of elevation • The angle between a horizontal line and the line of sight from an observer up to an object at a higher level. • Angle of depression • The angle between a horizontal line and the line of sight from an observer down to an object at a lower level.

  6. Example 3 • John wants to measure the height of a tree. He walks exactly 100 feet from the base of the tree and looks up. The angle of elevation to the top of the tree is 33°. How tall is the tree?

  7. Example 4 • A bird sits on top of a lamppost. The angle of depression from the bird to the feet of an observer standing away from the lamppost is 35°. The distance from the bird to the observer is 25 meters. How tall is the lamppost?

  8. Example 5 • An observer in the top of a lighthouse determines that the angles of depression to 2 sailboats directly in line with the lighthouse are 3.5 and 5.57degrees. If the observer is 125 feet above sea level, find the distance between the boats.

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