Question

the angle of elevation of the top of a hill from foot of a tower is 60 degree and the angle of depression form the top of tower to the foot of hill is 30 degree if tower is 50m high find the height of the hill

Answer 1

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Question: The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of top of the tower from the foot of the hill is 30°. If the tower is 50 m high, what is the height of the hill ?

Answer:

Required Height of the Hill is 150 metres.

Method of Solution:

In this Question, It is given that The angle of elevation of the top of a hill at the foot of a tower is 60° and the angle of elevation of top of the tower from the foot of the hill is 30°.

Given: Height of Tower = 50 metres

Now, Suppose h be the height of the hill and x m be the distance between the foot of the hill and foot of the tower,

Now, According to the Question's Statement,

Statement: the angle of elevation of the top of a hill from foot of a tower is 60 degree and the angle of depression form the top of tower with 30°.

Using Trigonometry Ratio:

In right Angled△ABC,

Cos 60° = x/h

x = h cot 60°.....(i)

In right angled△DBC,

cot 30° = x/50

x = 50 cot 30°........(ii)

Here, From both Equation has left hand Sides are Equal then their Right hand Sides will be equal.

From Equation (i) and (ii)

➡ h cot 60° = 50 cot 30°

➡ h = 50 cot 30°/cot 60°

➡ h = 50 × √3/1√3 = 50 × 3 = 150 m

Note: In Attachment, Building  Represent as Hill.

Hence, Height of the Hill is 150 metres

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