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 would it take further for him to reach the base of the tower?

Answer 1

Given :  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∘.

To find : Riding at the same speed, how long would it take further for him to reach the base of the tower

Solution:

Height of tower  =  15  m

Tan 30  =   Height of tower / Distance of cycle from base of tower

=> 1/√3 = 15 / Distance of cycle from base of tower

=> Distance of cycle from base of tower = 15√3 m

Tan 60  =   Height of tower / Distance of cycle from base of tower after 5 minutes

=> √3 = 15 / Distance of cycle from base of tower after 5 minutes

=> Distance of cycle from base of tower after 5 minutes  = 15/√3  = 5√3  m

Distance covered in 5 minutes =  15√3 - 5√3  = 10√3 m

remaining distance = 5√3  m

10√3 m  Distance covered in 5 minutes

1 m Distance covered in 5/10√3  min = 1/2√3  min

5√3 m  Distance covered in  = 5√3  / 2√3   = 2.5 mins

it will take 2.5 minutes more for him to reach the base of the tower

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