From the top of a storey-buliding, the angle of depression of a mango on a tree 20m away from the base of the storey building is 68^\circ. if the mango is 4.5 m above the ground, what is the height of the storey building to the nearest metre?
A
55m
B
54m
C
50m
D
49m
E
45m
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
From the figure above,
Tan\(\theta\) = \(\frac{\text{O}}{\text{A}}\)
Tan 68º = \(\frac{\text{x}}{20}\)
x = Tan 68º x 20 = 49.501m to 3 d.p
Height of Storey building = 49.501 + 4.5 = 54. 001 ≈ 54m to the nearest metre.
Source: Myschool Past Questions Archive (Record #41792)