Question

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 1

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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