From the top of a 12 m high building, the angle of elevation of the top of a tower is 60º and the angle of depression of the foot of the tower is ϴ, such that tanϴ = 3/4. What is the height of the tower?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 39.84 m
AB is the height of the building and CD is the height of the tower.
In right-angled triangle AEC, tanϴ = 3/4 = EC/AE
⇒ AE = 12 × 4 / 3 = 16 m
Now in the right-angled triangle AED,
tan 60º = √(3)/2 = DE/AE
⇒ DE = 8 × 1.73 = 13.84
so CD = 16 + 13.84 = 39.84 m