Question

A straight highway leads to the foot of a national communication and telecasting tower. A watchman standing at the top of the tower observes a car at an angle of depression of 30 which is approaching the foot of the tower with a uniform speed. 2 minutes later the angle of depression was found to be 60 degree. Then the watchman suspects that some terrorist are approaching the tower. It needs half a minute for the watchman to inform the security staff to be on the alert . How much time the car will take to reach the foot of the tower

Answer 1

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

Answer 2

Answer:

Explanation:

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