Question

A straight highway leads to the foot of a tower. A man 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. 10 seconds

later, the angle of depression of the car was found to be 60° . Find the

time taken by the car to reach the foot of the tower from this point.​

Answer 1

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∠PAB = 30°

After 6 sec,

∠PAC = 60°,∠ADB=90°

∠ABD =∠PAB so ∠ABD=30°

∠ACD =∠PAC so ∠ACD=60°

tan60° = AD/CD

AD =√3CD ……….(1)

tan30° = AD/CD

AD = BD/√3

√3CD = BD/√3

√3CD = BD

CD,= BC+CD

CD,= BC/2

Time taken to cover BC =,6Sec

Time taken to cover BC/2 = 6/2

Time taken to cover CD = 3sec

Hence it takes 3 sec to reach to the foot of the tower.

Answer 2

Dram diagram your own .