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A hook attached to a crane is 20 m above ground, and at an angle of elevation of 30° from a car. By how much should the hook be raised so that its angle of elevation with the car is increased to 60°? 

A hook attached to a crane is 20 m above ground, and at an angle of elevation of 30° from a car. By how much should the hook be raised so that its angle of elevation with the car is increased to 60°?  Correct Answer 40 m

Let the distance between the crane and the car be ‘x’ m

∵ tan θ = opposite/adjacent

⇒ tan 30° = 20/x

⇒ 1/√3 = 20/x

⇒ x = 20√3 m

Let the hook be raised by ‘y’ m to achieve an angle of elevation of 60° as shown below,

⇒ tan 60° = (y + 20)/x

⇒ √3 = (y + 20)/20√3

⇒ 20(3) = y + 20

⇒ y = 60 – 20 = 40 m

∴ The hook should be raised by 40 m

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