Posted by **vad** on Tuesday, January 4, 2011 at 12:57pm.

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 -
**drwls**, Tuesday, January 4, 2011 at 1:36pm
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 -
**Sbulu**, Tuesday, February 18, 2014 at 2:25am
Shut up

- trigonometry -
**chandler**, Thursday, January 1, 2015 at 5:08am
Right answer

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