An observer on the top of a tree, finds the angle of depression of a car moving towards the tree to be 30°. After 3 minutes this angle becomes 60°. After how much more time, the car will reach the tree?
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Answer:
Let the speed of the car be x units\min.
DC=3x
Let height be h
∠ACB=60
∠ADB=30
In right △ABC
tan60=
BC
h
∴h=
3
BC
In △ABD
tan60=
BD
h
∴h=
3
BD
BC+CD=
3
h
h+3x=
3
h
h(1−
3
)=−3x
3x=h(
3
−1)
h=
3
−1
3x
×
3
+1
3
+1
h=
2
3x(
3
+1)
Required time taken by car to reach the tower
=
speed
distance
=
x
BC
=
x
h
=
2x
3x(
3
+1)
=1.5(2.73)
=4min
hope you got it
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