Correct option is (b) 6 m
Let the height of tower = h
Angle of elevation at 3 m distance = α
Angle of elevation at 12 m distance = 90−α
Now, The line of sight, the ground and the tower will form a right angled triangle.
Thus, tan angle of elevation = \(\frac {\text{height }}{\text{distance}}\)
Thus, considering the 3 m distance,
tan α = \(\frac h3\) .....(1)
Considering the 12 m distance,
tan(90 − α) = \(\frac h{12}\) ......(2)
Multiplying the two equations,
tan α tan(90 − α) = \(\frac h3.\frac h{12}\)
tan α cot α = \(\frac h3.\frac h{12}\)
1 = \(\frac{h^2}{36}\)
h = 6 m