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?
Answers
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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Answer:
Total time taken by rider to move from B to C = 2 min, 30 sec.
Step-by-step explanation:
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