F3 MATHS題

B



A D

E


F G


H I

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The ramp is HFE and the elevation is 15 deg (angle EFGI 15 deg)
Andy’s eye level B is 1.6 m and Angel’s eye level A is 1.4 m from the ramp HFE.
AF = 1.4 m and BE = 1.6 m
Andy stands on E and Angel stands on F of the ramp. FE is 2 m apart.
Angle EFG = angle FHI = 15 deg.
sin angle EFG = EG/FE
sin 15 deg = EG/2 m
EG = 2m x sin 15 deg = 2 m X 0.2588 = 0.518 m
(a) vertical distance between their positions at the ramp is 0.518 m

The angle of depression of Angel's eyes from Andy's is the angle made between line AB and horizontal line drawn through B. This angle is the same as angle BAD. (alternate angles)
We have to find angle BAD.
cos angle GFE = FG/FE
cos 15 deg = FG/2 m
FG = 2 m x cos 15 deg = 2m x 0.9659 = 1.9318 m
AD = FG = 1.93 18 m
BG = BE + EG = 1.6 m + 0.5198 m = 2.119 m
AF = 1.4 m, DG = 1.4 m
BD = BG – DG = 2.119 m – 1.4 m = 0.719 m
tan angle BAD = BD/AD = 0.719 m/1.9318 m = 0.3722
Angle = tan^1 (0.3722) = 20.4 deg
The angle of depression of Angel's eyes from Andy's is 20.4 deg