Question

A man standing on the deck of a ship, which is 10 m above the water level,observes the angle of elevation of the top of a hill as 60° and the angle of depression of the base of the hill as 30°.calculate the distance of the hill from the ship and the height of the hill? ​

Answer 1

Given :-

• Angle of elevation of the top of a hill = 60°
• Angle of depression of the base of the hill = 30°
• A man standing on the deck of a ship = 10 m

Find :-

• Calculate the distance of the hill from the ship .
• The height of the hill.

SoLuTioN :-

Let the height of the distance of the hill from the ship = x

• AB = 10 m

Let CE be the hill.

CD = AB = 10m

In △ADE

we have ,

↬ tan 60° = DE/AD

where,

• tan60° = √3

↠ √3 = h/x

↠ h = √3x ....... ( eq - 1 )

In △ ABC ,

we have

↬ tan 30° = AB / BC

where ,

• tan 30° = 1/√3

↠ 1/√3 = 10/x

↠ X = 10√3 ......... ( eq - 2 )

↬ The distance of the hill from the ship is 10√3 metres .

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Now,

putting the values of x in equation (1) we get,

↠ h = √3 × 10√3

↠ h = 30 m

↠DE = 30m

Now, let's find the

The height of the hill from the ship :-

As from the above figure :-

↠ CE = CD + ED

↠ 10 + 30

↠40 metres .

Therefore ,

The distance of the hill from the ship is 10√3 metres .

The height of the hill is 40 metres .

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