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?
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.
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