Answer :

Given:

Angle of depression 1 (say PAB) = 30o


Angle of depression 2 (say PAC) = 60o


Time (say t) = 6 seconds


Let, Height of man and tower = AD



the tower is vertical


ADB = 90°


Now,


PABD


AB is transversal


∴∠ABD = PAB = 30° [Alternate Angles]


Similarly,


PABD


AC is transversal


∴∠ACD = PAC = 60° [Alternate Angles]


In ∆ABD,




…(1)


Similarly,


In ∆ACD,




…(2)


From (1) and (2),



BD = 3×√3×CD


BD = 3CD


BC + CD = 3CD


BC = 3CD CD


BC = 2CD



Now,


Time taken to cover BC = 6 seconds


Time taken to cover CD(1/2BC) =1/2× 6 seconds = 3 seconds


Hence, the time taken to reach the foot of tower from C = 3 seconds


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