Question

There are two poles,one each on either bank of river ,just opposite to each other.One pole is 60 m high. From the top of this pole, the angles of depression of the top and the foot of the other pole are 30° and 60° . Find the width of the river and the height of the pole

Answer 1

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Answer 2

Answer:

The width of river is 34.6410 m

The height of another pole is 80 m.

Step-by-step explanation:

Refer the attached figure.

The two poles are AB and EC

AB = 60 m

∠DBC = 60°

∠EBD = 30°

∠DBC = ∠BCA = 60° (Vertically opposite angles)

AC = width of river

In ΔABC

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

$Tan 60^{\circ} = \frac{AB}{AC}$

$\sqrt{3} = \frac{60}{AC}$

$AC= \frac{60}{\sqrt{3}}$

Thus the width of river is$\frac{60}{\sqrt{3}}$ = 34.6410 m

In ΔBED

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

$Tan 30^{\circ} = \frac{ED}{BD}$

$\frac{1}{\sqrt{3}} = \frac{ED}{\frac{60}{\sqrt{3}}}$

$ED =20$

EC =ED+DC=20+60=80

Thus the height of another pole is 80 m.