Question

the pilot of an aeroplane at an altitude of 200 metres observes the angle of depression of opposite points on the two banks of river to be 45 degree and 60 degree. find the width of the river

Answer 1

It is 315.47 metres approx.

Answer 2

according to the attachment ,

tan60 = AD/CD

√3 = 200m/CD

CD × √3 = 200m

CD = 200m/√3
___________________

tan45 = AD/BD

1 = 200m/BD

BD = 200m
___________________

width of the river = BC = ?

BC = BD+CD

BC = 200m+200m/√3

BC = 200m(1 + 1/√3)

BC = 200(√3+1/√3) m

BC = 315.47 (approximate)
_______________________

so the width of the river = BC ≈ 315.47 m