A vertical pole and a vertical tower are on the same level ground in such a way that, from the top of the pole, the angle of elevation of the top of the tower is 60º and the angle of depression of the bottom of the tower is 30º. If the height of the pole is 24m, then find the height of the tower (in m).
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 96.
Let CE be the tower & AB be the pole
As given in the question AB = 24 m
Therefore, In △ADC, tan 30° = CD/AD
⇒ AD = CD × (3)1/2
And CD = AB = 24. Therefore, AD = 24 × (3)1/2
Now, in △ADE, tan 60° = ED/AD
⇒ (3)1/2 = ED/(24 × (3)1/2)
∴ Height of tower = CE = 24 × (3)1/2 × (3)1/2 = 96 m