Question

from the top of a light house, it is observed that a ship is sailing directly towards it and the angle of depression of the ship changes from 30° to 45° in 10 minutes. Assuming that the ship is sailing with uniform speed ; calculate in how much more time (in minutes) will the ship reach the light house?

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

In ΔABD

$\\ tan$θ = $\frac{Perpendicular}{Base}$

$\\ tan30$° = $\frac{AB}{BD}$

$\frac{1}{\sqrt{3} } = \frac{H}{BD}$

$BD = \frac{H}{\frac{1}{\sqrt{3}}}$

In ΔABC

$\\ tan$θ =  $\frac{Perpendicular}{Base}$

$\\ tan45$° = $\frac{AB}{BC}$

$\\ 1 =$ $\frac{H}{BC}$

$\\ BC = H$

Now distance travelled in 10 minutes = $\\ BD - BC$

                                                              = $H\sqrt{3} - H$

$\\ Speed = \frac{Distance}{Time}$

$\\ Speed = \frac{H\sqrt{3} - H}{10}$

If the ship reaches the light house then the distance becomes 0 from H

So,

$Time = \frac{Distance}{Speed}$

$Time = \frac{\frac{H - 0}{H\sqrt{3} - H}}{10}$

$Time = 13.66$