Question

A cyclist observes that the angle of elevation of the top of a tower of height 15 m is 30∘. After 5 minutes, the angle of elevation is 60∘. Riding at the same speed, how long (in sec) would it take further for him to reach the base of the tower?​

Answer 1

Let the Height of the Tower be AD=h

and let the height of Building be CE=15

In △ADE

⇒tan60=

DE

AD

=

DE

h

⇒DE=

3

h

and we can see that BCDE is a Rectangle

⇒BC=DE=

3

h

and BD=CE

so, in △ABC

⇒tan30

o

=

BC

AB

=

h/

3

AB

⇒h=3AB⇒AB=

3

h

Now, it is given that CE=15⇒AD−AB=15⇒h−

3

h

=

3

2h

=15⇒h=22.5 m

and DE=

3

h

=

3

22.5

=13 m (Take

3

=1.73)

Answer 2

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A cyclist observes that the angle of elevation of the top of a tower of height 15 m is 30∘. After 5 minutes, the angle o...

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