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 $\sqrt{3}=1.73$)
Answer & explanation
Correct answer: option 3
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