8 5 Angles of Elevation Depression Angles of

8 -5 Angles of Elevation & Depression

Angles of Elevation n Angle of Elevation: The angle between the line of sight and the horizontal when an observer looks upward. ht Sig f eo n i L Angle of Elevation

Example 1 n 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° 7. 6 m 18. 2 m

Angle of Depression n Angle of Depression: The angle between the line of sight when an observer looks downward and the horizontal. Angle of Depression ht Sig f eo n i L

Example 2 n 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 3 m Sin 6° = x/3 6° ? 3(Sin 6°) = x 31. 4 cm = x

Example 3 n 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/x 1 (Tan 7°) = 75 7° x 1 = 75/Tan 7° x 1 ≈ 610. 8 75 m 12. 5° Tan 12. 5° = 75/x 2 (Tan 12. 5°) = 75 x 2 = 75/Tan 12. 5° x 2 ≈ 338. 3 12. 5° Answer = x 1 – x 2 = about 273 m 7°

Try these n n n n p. 466 #1 Answer: about 2. 2° #2 Answer: about 169. 9 m #3 Answer: C…x = 150/tan 12° Homework #53 p. 467 4 -18 even, 19 -21, 27 -28