Question

A man in a boat rowing away from a lighthouse,150 m high takes 1.5 minutes to change the angle of elevation of the top of the lighthouse from 60 to 45 degrees. Find the speed of the boat.

Answer 1

here is my answer
I hope it will help you

Answer 2

Answer:

Speed = 42.26 m / min.

Step-by-step explanation:

Refer the attached file

Height of lighthouse i.e. AB = 150 m

The angle of elevation initially , ∠ACB = 60 °

Distance of boat from the base of the lighthouse = BC

Changed angle of elevation , ∠ADB = 45°

Now, Distance of  boat from the base of the lighthouse = BD

Distance traveled by boat in 1.5 minutes = CD = BD-BC

In ΔABD

$Tan\theta = \frac{Perpendicular}{Base}$

$Tan45^{\circ}= \frac{AB}{BD}$

$1 = \frac{150}{BD}$

$BD =150$

In ΔABC

$Tan\theta = \frac{Perpendicular}{Base}$

$Tan60^{\circ}= \frac{AB}{BC}$

$\sqrt{3} = \frac{150}{BC}$

$BC=\frac{150}{\sqrt{3}}$

So, Distance traveled by boat in 1.5 minutes :

CD = BD-BC

$CD=150-\frac{150}{\sqrt{3}}$

$CD=\frac{150\sqrt{3}-150}{\sqrt{3}}$

$CD=\frac{150\times3-150\sqrt{3}}{3}$

$CD=\frac{450-150\sqrt{3}}{3}$

Speed = Distance / time

Speed = $\frac{\frac{450-150\sqrt{3}}{3}}{1.5}$

Speed = 42.26 m / min.

Thus the speed of the boat is 42,26 m /min