Question

From the top of a hill 200m high, the angles of depression of the top and the bottom of a pillar are 30°and 60° respectively. Find the height of the pillars and uts distance from the hill.

Answer 1

Answer of the question is shown below.....
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Answer 2

Answer:

The height of the pillars is 133.33 m  and  its distance from the hill is 115.47 m

Step-by-step explanation:

Refer the attached figure

Height of Hill = AC = 200 m

Let BC = ED = h

So, AB = 200-h

The angles of depression of the top and the bottom of a pillar are 30°and 60° respectively.i.e. ∠AEB = 30° and ∠ADC = 60°

BE = CD = Distance between hill and pillar

In ΔABE

$Tan \theta = \frac{Perpendicular}{Base}$

$Tan 30^{\circ}= \frac{200-h}{BE}$

$\frac{1}{\sqrt{3}}= \frac{200-h}{BE}$

$BE=(200-h)\sqrt{3}$   --1

In ΔADC

$Tan \theta = \frac{Perpendicular}{Base}$

$Tan 60^{\circ}= \frac{AC}{CD}$

$\sqrt{3}= \frac{200}{CD}$

$CD= \frac{200}{\sqrt{3}}$    ---2

$CD=115.47$

So, its distance from the hill is 115.47 m

Equating 1 and 2

$(200-h)\sqrt{3}= \frac{200}{\sqrt{3}}$

$(200-h)3=200$

$600-3h=200$

$400=3h$

$\frac{400}{3}=h$

$133.33=h$

Hence the height of the pillars is 133.33 m  and  its distance from the hill is 115.47 m