A maths teacher standing on first floor of the school building looks at the student on the ground approching forwards the school building in uniform speed angle of depression was 30*. After 12 second the angle of depression between teacher and student becomes 60* Calculate time require by student to reach the building
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let the distance of ground till the first floor of building be ab
so, d is the student at uniform speed with angle of depression 30
join a to d, b to d
after 12 seconds
mark a point between b and d as c. with angle of depression 60
angle adc =30,. angle acb =60
in triangle acb,tan 60=ab\ bc by cross multiplication bc=ab\√3
in triangle abd tan 30=ab\bc+cd 1\√3=ab\bc+12
bc+12=ab√3
ab\√3 +12=ab√3
ab+12√3 \√3 =ab√3
ab+12√3=3ab
12√3=2ab
6√3=ab bc=ab\√3 so, bc=6√3\√3 = 6 seconds
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