# trigonometry

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An aeroplane at an altitude of 200m observes the angles of depression of opposite points on the two banks of a river to be 45 degree and 60 degree. Find in metres, the width of river.

• trigonometry -

Let H be the altitude (which you already know), and D be the horizontal distance from the plane to the nearest bank of the river. Let w be the width of the river.

H/D = tan 60
H/(D + w) = tan 45

Not that the second equation implies that
H = D + w
and the first equation implies that
H = sqrt3 * D

Solve for w in terms of H, using substitution to eliminate D.

H = H/sqrt3 + w

H(1 - 1/sqrt3) = w

• trigonometry -

Shut up

• trigonometry -

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