Question

The angle of elevation of the top of a pillar from
a point on the ground is 15° on walking 100 m
towards the tower, the angle of elevation is
found to be 30°. Calculate the height of the tower
(where tan 15° = 2 -V3).​

Answer 1

Answer :-

50 m

Solution :-

[ Refer to attachment ]

Height of the pillar = AB

Angle of elevation of the top of a pillar from a point ∠ACB = 15°

Distance walked by the person ( CD ) = 100 m

Angle of elevation of the top of a pillar after walking 100 m distance ∠ADB = 30°

Consider Δ ADB

==> tan 30° = P / B

==> 1 / √3 = AB / DB

==> DB = √3 . AB --- EQ ( 1 )

Consider Δ ABC

==> tan 15° = P / B

==> 2 - √3 = AB / ( CD + DB)

==> 2 - √3 = AB / ( 100 + DB)

==> 1 / ( 2 + √3 ) = AB / ( 100 + DB )

[ Because , After rationalising 2 - √3 we get 1 / ( 2 + √3 ) ]

==> 100 + DB = 2AB + √3AB

==> DB = 2AB + √3AB - 100 ---- EQ( 2 )

From EQ( 1 ) & EQ( 2 )

==> 2AB + √3AB - 100 = √3.AB

==> 2AB - 100 = 0

==> 2AB = 100

==> AB = 50

Therefore the height of the pillar is 50 m.

Answer 2

Step-by-step explanation:

Aloha !

Take tan .

Now,

tan 30°=h/y

1/√3=h/y

y=√3h

Now ,.

tan15°=h/100+y

2-√3=h/100+y

2-√3=h/100+√3h

h=100/2

h=50/1

h=50m

Thank you

@ Twilight Astro ✌️☺️❤️