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8-5 Angles of Elevation & Depression

8-5 Angles of Elevation & Depression. Line of Sight. Angle of Elevation. Angles of Elevation. Angle of Elevation : The angle between the line of sight and the horizontal when an observer looks upward. 7.6 m. 18.2 m. Example 1.

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8-5 Angles of Elevation & Depression

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  1. 8-5 Angles of Elevation & Depression

  2. Line of Sight Angle of Elevation Angles of Elevation • Angle of Elevation: The angle between the line of sight and the horizontal when an observer looks upward.

  3. 7.6 m 18.2 m Example 1 • Find the angle of elevation of the Sun when a 7.6 meters flagpole casts a 18.2 meter shadow. Round to the nearest tenth of a degree. Tan = Opposite/Adjacent Tan x = 7.6/18.2 x = tan-1 (7.6/18.2) x = 22.7°

  4. Angle of Depression Line of Sight Angle of Depression • Angle of Depression: The angle between the line of sight when an observer looks downward and the horizontal.

  5. 3 m ? 6° Example 2 • A wheelchair ramp is 3 meters long and inclines at 6°. Find the height of the ramp to the nearest tenth of a centimeter. Sin = Opposite/Hypotenuse Sin 6° = x/3 3(Sin 6°) = x 31.4 cm = x

  6. 7° 12.5° 75 m 7° 12.5° Example 3 • Two boats are observed by a parasailer 75 meters above a lake. The angles of depression are 12.5° and 7°. How far apart are the boats? Tan 7° = 75/x1 x1 (Tan 7°) = 75 x1 = 75/Tan 7° x1 ≈ 610.8 Tan 12.5° = 75/x2 x2 (Tan 12.5°) = 75 x2 = 75/Tan 12.5° Answer = x1 – x2 = about 273 m x2 ≈ 338.3

  7. Try these • p. 466 #1 • Answer: about 2.2° • #2 • Answer: about 169.9 m • #3 • Answer: C…x = 150/tan12° • Homework #54 p. 467 4-18 even, 19-21, 27-28

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