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

Answer:

13.66 minutes

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:-

In ΔABD

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

$\\ tan$$\\ 30$° = $\frac{AB}{BD}$

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

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

In ΔABC

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

$\\ Tan 45$° = $\frac{AB}{BC}$

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

$\\ BC = H$

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 lighthouse then the distance becomes 0 from H

So,

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

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

$\\ Time = 13.66$