Vertical observation tower observes a car moving at uniform speed coming directly towards it if it takes 12 minutes for the angle of depression to change from the details of the 45 degree how long will the car take to reach the observation tower from this.
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Now consider the triangle ,ABD
tan 30° = AB/BD
1/√3 =AB / BD
BD/ √3 = AB
BC + CD /√3 + AB....(1)
In Δ ABC
tan 45° = AB/BC
1 = AB/BC
AB =BC ..(2)
substitute the value of BC from equation (1) & (2)
Ab + CD/ √3 =Ab
Ab + CD =√3 AB
√3 AB -AB =CD
AB (√3 -1) = CD...(3)
The car takes 12 min to cover the distance CD
CD= 12v...(4)
Putting the value of CD in equation (4)
AB (√3-1) = 12v
AB (√3 -1)/12 = v...(5)
time taken by the car to cover the distance BC
Time = Distance / Speed
Time = BC/ AB (√3 -1 )
Time = 12 AB / AB (√3-1)
Time = 12 / √3-1
≈ 16.4 minutes
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