Question

there are two poles one each on either bank of a river just opposite to each other one pole is 60 m high from the top of a this pole the angles of depression of the top and the foot of the other pole are 30 degree and 60 degree respectively find the width of the river and height of other pole

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Answer: Width of the river is 34.64 m.and The height of the other pole is 20 m.

Step-by-step explanation:

Since we have given that

Length of one pole = 60 m

Angle of depression of the top = 30

Angle of depression of the foot of the other pole = 60

As shown in the figure:

In ΔABC,

$\tan 60^\circ=\frac{AB}{BC}\\\\\sqrt{3}=\frac{60}{BC}\\\\BC=\frac{60}{\sqrt{3}}=34.64\ m$

Hence, width of the river is 34.64 m.

And now consider, Δ BDC,

$\tan 30^\circ=\frac{CD}{BC}\\\\\frac{1}{\sqrt{3}}=\frac{CD}{\frac{60}{\sqrt{3}}}\\\\CD=\frac{60}{\sqrt{3}\times \sqrt{3}}\\\\CD=20\ m$

Hence, the height of the other pole is 20 m.