8-5 Angles of Elevation & Depression

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

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 7.6 m 18.2 m Tan x = 7.6/18.2 x = tan-1 (7.6/18.2) x = 22.7°

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

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 6° ? 3 m Sin 6° = x/3 3(Sin 6°) = x 31.4 cm = x

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 75 m 7° 12.5° 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

Try these p. 466 #1 Answer: about 2.2° #2 Answer: about 169.9 m #3 Answer: C…x = 150/tan12° Homework #53 p. 467 4-18 even, 19-21, 27-28