Question 94

A man on the top of a tower, standing on the sea-shore, finds that a boat coming towards him takes 10 minutes for the angle of depression to change from $$30^\circ$$ to $$60^\circ$$. How soon the boat reach the sea-shore ?

Solution

height of tower = h

$$\tan 30\degree = \frac{h}{x+y}$$

$$\tan 60\degree = \frac{h}{x}$$

$$\frac{h}{\surd{3}} = x$$

$$\frac{1}{\surd{3}} = \frac{h}{x+y}$$

$$h\surd{3} = x+y $$

$$h\surd{3} =\frac{h}{\surd{3}} +y $$

$$\frac{2h}{\surd{3}} = y$$

y = 2x

time taken to travel y distance = 10mins

time taken to travel x distance ( half of y distance) = 5 mins

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