Question

An aeroplane at an altitude of 300 m observes the angles of depression of opposite points on the

two banks of a river to be 450

and 600

. Find the width of the river.

Answer 1

35/2km in 5hours. find speed in meter/ second

Answer 2

Answer:

The width of the river is 473.2 m

Step-by-step explanation:

Refer the attached figure .

Height of Airplane i.e.AB = 300 m.

An airplane at an altitude of 300 m observes the angles of depression of opposite points on the  two banks of a river to be 45° and 60°.

i.e. ∠ACB = 45°

∠ADB=60°

So, in ΔABC

Using trigonometric ratios  

$tan\theta = \frac{Perpendicular}{Base}$  

$tan45 ^{\circ} = \frac{AB}{CB}$  

$1 = \frac{300}{BC}$  

$BC=300$

In ΔABD

Using trigonometric ratios  

$tan\theta = \frac{Perpendicular}{Base}$  

$tan 60 ^{\circ} = \frac{AB}{BD}$  

$\sqrt{3} = \frac{300}{BD}$  

$BD = \frac{300}{\sqrt{3}}$

$BD =173.20$

So, width of river = CB+BD=300+173.20=473.2 m

Hence the width of the river is 473.2 m