The angle of elevation of the top of an unfinished tower at a point distant 78 m from its base is 30°. How much higher must the tower be raised (in m) so that the angle of elevation of the top of the finished tower at the same point will be 60°?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 52√3
Let the Initial height of the unfinished tower be h, and the base given as 78 m
then according to question,
tan 30° = h/78
1/√3 = h/78
h = 78/√3 = 78√3/3 = 26√3 m
Now let the height that it must be raised be x, then for the angle of elevation 60°, as the base is constant
tan 60° = (26√3 + x)/78
√3 = (26√3 + x)/78
x = 78√3 - 26√3 = 52√3 m