The angle of elevation of the top of a tower from a point on the horizontal is 30°. If the observer moves 20 m towards the tower, the angle of elevation of the top of the tower increases by 15°. The height of the tower is : (Take $\sqrt{3}=1.73$)

27.3 m

º

In triangle ABC ,

tan45º = \(\frac{AB}{BC}\) = 1

Let us consider that,

AB = BC = x

In triangle ABD ,

tan30º = \(\frac{AB}{BD}\) = \(\frac{1}{√3}\)

\(\frac{x}{20 + x}\) = \(\frac{1}{√3}\)

√3x - x = 20

( 1.73 - 1 )x = 20

x = \(\frac{20}{0.73}\)

= 27.3

The correct answer is option (3) : 27.3 m