Question
An aeroplane at an altitude of 200 metres observes the angles of depression of opposite points on the two banks of a river to be 45° and 60°. Find the width of the river.
Solution
Let the position of the aeroplane be A, B and C be two points on the two banks of a river such that the angles of depression at B and C are 45° and 60° respectively. Let BD = x m, y m andAD = 200 m.
In right triangle ABD, we have
In right triangle ACD, we have
Adding (i) and (ii), we get
Hence, the width of the river is 315.4 metres.
In right triangle ABD, we have
In right triangle ACD, we have
Adding (i) and (ii), we get
Hence, the width of the river is 315.4 metres.
