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°. if the mango is 4.5 m above the ground, what is the height of the storey building to the nearest metre?
- 55m
-
54m
- 50m
- 49m
- 45m
The correct answer is: B
Explanation
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.