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A man in a boat rowing away a lighthouse 100 m height takes 2 m to change the angle of elevation of the top at the lighthouse from 60 to 30. Find the speed of the boat in metres per minute.(3=1.732).

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: Distance = Speed \times Time
tan\theta = OppositeAdjacent
tan60=3
tan30=13

Complete step-by-step answer:
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We construct the question as a diagram to understand easily.
Consider ΔABD,
Here AB is a height of the lighthouse is 100 m. A be the top of the lighthouse, B be the bottom of the light house. CD be the distance which man travelled to change the angle of elevation.
Let x be the speed of the boat metres per minute.
CD=y=2x (Distance = speed \times time)
AB=100m
Now we are going to find the distance between CB using the tangent formula,
From ACB, opposite side is AB and adjacent side is CB.
Consider ACB=60,
By using the tangent formula in ACB we get,
tan60=ABCB
Substituting the value of tan60=3 and AB=100m we get,
3=100CB
Let us solve this for CB,
CB=1003
CB=1001.732 (For 3=1.732)
CB=57.73
 Now we are going to find the distance between DB using the tangent formula,
From ADB, opposite side is AB and adjacent side is DB.
Consider ADB=30,
By using the tangent formula in ADB we get,
tan30=ABDB
Substituting the value of tan30=13 and AB=100m we get,
13=100DB
Let us solve this for DB,
DB=100×3
DB=100×1.732 (For 3=1.732)
DB=173.2
Consider,
CD=DBCB
Substituting the values of DB=173.2 and CB=57.73 we get,
 CD=172.357.73
CD=115.47
Since, CD=y=2x (Distance = speed \times time)
CD=y=2x=115.47
Let us solve this for x we get,
x=115.472
x=57.73 m/min

The speed of the boat in metres per minute is 57.73 m/min

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.