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Angles of Elevation and Depression

Angles of Elevation and Depression. Angle of Elevation. Line to horizon. Suzie is looking at a hot-air balloon floating overhead. The angle of her line of sight is the “ Angle of Elevation .”. Line to horizon. Angle of Depression. Josh is in the balloon and is looking down at Suzie.

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Angles of Elevation and Depression

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  1. Angles of Elevation and Depression

  2. Angle of Elevation Line to horizon Suzie is looking at a hot-air balloon floating overhead. The angle of her line of sight is the “Angle of Elevation.”

  3. Line to horizon Angle of Depression Josh is in the balloon and is looking down at Suzie. The angle of his line of sight is the “Angle of Depression.”

  4. What is the relationship between the Angle of Elevation and Angle of Depression? Angle of Depression Angle of Elevation They are congruent.

  5. 1 is the angle of depression from the airplane to the building. 2 is the angle of elevation from the building to the airplane. Describe 1 and 2 as they relate to the situation shown.

  6. Draw a diagram to represent the situation. x 200 tan 35° = Use the tangent ratio. Solve for x. x = 200 • tan 35° Use a calculator. 200 35 140.041508 So x 140. A surveyor stands 200 ft from a building to measure its height. The angle of elevation to the top of the building is 35°. How tall is the building? The building is about 140 ft tall.

  7. An airplane flying 3500 ft above ground begins a 2° descent to land at an airport. What is the “line of sight” distance from the airplane to the airport when it starts its descent? Draw a diagram to represent the situation. 3500 x sin 2° = Use the sine ratio. Use a calculator. 3500 sin 2° 3500 2 100287.9792 x = Solve for x. Divide by 5280 to convert feet to miles. 5280 18.993935 The airplane is about 19 mi from the airport when it starts its descent.

  8. Now it’s your turn!!! Use the diagram for Exercises 1 and 2. 1. Describe how 1 relates to the situation. 2. Describe how 2 relates to the situation. angle of elevation from man’s eyes to treetop angle of depression from treetop to man’s eyes A 6-ft man stands 12 ft from the base of a tree. The angle of elevation from his eyes to the top of the tree is 76°. 3. About how tall is the tree? 4. If the man releases a pigeon that flies directly to the top of the tree, about how far will it fly? 5. What is the angle of depression from the treetop to the man’s eyes? about 54 ft (48 ft plus 6 ft for the height of the man.) about 50 ft 76°

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