
A man in a boat rowing away a lighthouse height takes to change the angle of elevation of the top at the lighthouse from to . Find the speed of the boat in metres per minute. .
Answer
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Hint: We have to find the speed of the boat, to calculate speed we need to find the distance that boat travelled from the lighthouse. We find the distance by using the angle elevation and tangent formula. After finding the distance we can find the speed of the boat in metres per minute.
Formula used:
Complete step-by-step answer:
We construct the question as a diagram to understand easily.
Consider ,
Here is a height of the lighthouse is . be the top of the lighthouse, be the bottom of the light house. be the distance which man travelled to change the angle of elevation.
Let be the speed of the boat metres per minute.
Now we are going to find the distance between using the tangent formula,
From , opposite side is and adjacent side is .
Consider ,
By using the tangent formula in we get,
Substituting the value of and we get,
Let us solve this for ,
(For )
Now we are going to find the distance between using the tangent formula,
From , opposite side is and adjacent side is .
Consider ,
By using the tangent formula in we get,
Substituting the value of and we get,
Let us solve this for ,
(For )
Consider,
Substituting the values of and we get,
Since,
Let us solve this for we get,
The speed of the boat in metres per minute is
Note: The term angle of elevation denotes the angle from the horizontal upward to an object. An observer’s line of sight would be above the horizontal. In this question we may go wrong on finding the speed of the boat and we will be careful on substituting the values. Given is already in required unit values. So we don’t change the unit values for speed and distance.
Formula used:
Complete step-by-step answer:

We construct the question as a diagram to understand easily.
Consider
Here
Let
Now we are going to find the distance between
From
Consider
By using the tangent formula in
Substituting the value of
Let us solve this for
Now we are going to find the distance between
From
Consider
By using the tangent formula in
Substituting the value of
Let us solve this for
Consider,
Substituting the values of
Since,
Let us solve this for
Note: The term angle of elevation denotes the angle from the horizontal upward to an object. An observer’s line of sight would be above the horizontal. In this question we may go wrong on finding the speed of the boat and we will be careful on substituting the values. Given is already in required unit values. So we don’t change the unit values for speed and distance.
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