Question

The lower 24 m portion of a 50 m tall tower is painted green and the remaining portion red. What is the distance of a point on the ground from the base of the tower where two different portions of the tower subtend equal angles?

(a) 60 m

(b) 72 m

(c) 90 m

(d) 120 m

Answer 1

Correct option is (d) 120 m

Let AC be the tower whose length is 50 m.

Let AB = 24 m and BC = 26 m

In rt. \(\triangle\)ABD,

\(\tan \theta = \frac{AB}{AD}\)

⇒ \(\tan\theta =\frac{AB}{AD}\)

⇒ \(\tan\theta =\frac{24}{x}\)  

In rt. \(\triangle\)ACD,