A vertical pole and vertical tower are on the same level of the ground in such a way that from the top of the pole, the angle of elevation of the top of the tower is 60° and the angle of depression of the bottom of the tower is 30°. If the height of the tower is 76 m, then find the height (in cm) of the pole.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 19
The angle of elevation of the top of the tower from the top of the pole = 600
The angle of depression of the bottom of the tower from the top of the pole = 300
Let the height of the pole (AB) = CD = x m
The height of ED = (76 - x) m
In ΔACD -
tan 300 = CD/AD
1/√3 = x/AD
AD = √3x .....(1
In ΔAED -
tan 600 = ED/AD
√3 = (76 - x)/√3x
76 - x = 3x
3x + x = 76
4x = 76
x = 76/4 = 19