Question

An aeroplane is flying at a height of 300m above the ground. Flying at this height,the angle of depression from the aeroplane of two points on banks of a river in opposite directions are 40° and60° respectively. Find the width of the river? (root3=1.732)

Answer 1

Solution:

Let P be the position of the aeroplane and let A and B be

two points on the two banks of a river such that the angle of depression at A and B are 60°

and 45° respectively.

Let AM = x m and

BM = y m.

We have to find ,

Width of the river AB .

i) In ∆APM, we have

tan60° = PM/AM

=> √3 = 300/x

=> x = 300/√3

Rationalising the denominator, we get

= [(300×√3)/(√3×√3)

= 300√3/3

= 100√3

= 100×1.732

= 173.2 m ----(1)

ii) In ∆BPM, we have

tan45° = PM/BM

=> 1 = 300/y

=> y = 300 m----(2)

From equations (1) & (2) , we get

AB = x+y

= 173.2 + 300

= 473.2 m

Therefore,

The width of the river = 473.2 m

••••

Answer 2

Step-by-step explanation:

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