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A man on the top of a tower standing on the seashore find the

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A man on the top of a tower standing on the seashore find the a boat coming towards him takes $10$ minutes for the angle of depression to change for $3 0^{0}$ to $6 0^{0}$ Find the time(in mimutes) taken by the boat to reach the shore from this position

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A man on the top of a tower standing on the seashore find the a boat coming towards him takes

10

minutes for the angle of depression to change for

3 0^{0}

6 0^{0}

Find the time(in mimutes) taken by the boat to reach the shore from this position

6 mins ago

Discuss this question LIVE

6 mins ago

Text solutionVerified

Let AB be the tower and C and D be the two position of the boat
Let AB = h, CD = x and AD = y

\frac{h}{y} = tan 6 0^{0} = 3 \Rightarrow y = \frac{h}{3}

\frac{h}{x + y} = tan 3 0^{0} = \frac{1}{3} \Rightarrow x + y = 3 h

∴ x = (x + y) - y = (3 h - \frac{h}{3}) = \frac{2 h}{3}

Now

\frac{2 h}{3}

is covered in 10 min

∴ \frac{h}{3}

will be covered in

(10 \times \frac{3}{h} \times \frac{h}{3}) = 5 min

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Question Text	A man on the top of a tower standing on the seashore find the a boat coming towards him takes $10$ minutes for the angle of depression to change for $3 0^{0}$ to $6 0^{0}$ Find the time(in mimutes) taken by the boat to reach the shore from this position
Answer Type	Text solution:1
Upvotes	150