Question

A man in a boat rowing away from a lighthouse 100m high takes 2 minutes to change angle of elevation of the top of a lighthouse from 60 degree to 30 degree find the speed of boat in metres per minute.

Answer 1

Speed of the boat will be 36.6 m/min

Step-by-step explanation:

We have given height h = 100 m

Initially angle is $60^{\circ}$

Let the initial distance is x m

So $tan60^{\circ}=\frac{100}{x}$

$x=\frac{100}{\sqrt{3}}=57.737m$

Now after 2 minutes angle will become 30°

And let the distance is y m

So $tan30^{\circ}=\frac{100}{y}$

$y=100\sqrt{3}=173.2m$

So distance traveled in 2 minutes = 173.2 - 100 = 73.2 m

So speed $=\frac{distance}{time}=\frac{73.2}{2}=36.6m/min$

Speed of the boat will be 36.6 m/min

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A man in a boat rowing away from a lighthouse 150m high,takes 2 minutes to change the angle of elevation of the top of the lighthouse from 60 to 45 degree. Find the speed of the boat.

https://brainly.in/question/2363709

Answer 2

Answer:

Step-by-step explanation:

ACB = 60⁰ and  ADB = 30⁰

Let, the length of CD = x m

And the length of CB = y m

⇒     y = 57.73 m    

⇒  x + y = 173 m

⇒ x = 115.27 m

Speed of the boat = Distance/Time

= 57.635 m/min