Question

The angle of elevation of a bird from the eye of a man on the bank of a pond is 30 and
the angle of depression of its reflection in the pond is 60. Find the height of the bird
above the pond if the distance of the eye from the foot of the man is 1.5 metres​

Answer 1

Answer:

1.5 m

Step-by-step explanation:

Let the bird be A

the eye be C

the reflection be D

Assuming reflection is on the surface of water,

Then the man's feet and reflection are on ground(same) level

Therefore man's height = perpendicular distance from reflection(BD)

Remaining in the picture

Thank you

Answer 2

The height of the bird  above the pond is 75 m

Step-by-step explanation:

let the bird be at the point C and the angle of elevation from A

height above the lake BE = 60 m

let the height of the bird be  CE = h m

reflection of the bird in the lake F will be at a distance h m then

AD = BE = x m

AB = 50 m

CD = (h-50 ) m

then in triangle ADC

$\theta = 30^\circ \\\\\tan 30 ^\circ = \frac{CD}{AD}\\\\\frac{1}{\sqrt{3}}= \frac{h-50}{x}\\\\x = \sqrt{3}h - 50\sqrt{3}...(1)$

now, in triangle ADF

$\theta = 60^\circ \\\\\tan 60 ^\circ = \frac{DF}{AD}\\\\{\sqrt{3}= \frac{h}{x}\\\\x =\frac{h}{\sqrt{3}} ...(2)$$\theta = 60^\circ \\\\\tan 60 ^\circ = \frac{DF}{AD}\\\\\sqrt{3}= \frac{h}{x}\\\\x =\frac{h}{\sqrt{3}} ...(2)$

from 1 and 2

$\frac{h}{\sqrt{3}} = \sqrt{3}h - 50 \sqrt{3}\\\\h = 3h-50\times 3\\\\2h = 150\\\\h = 75$

hence , The height of the bird  above the pond is 75 m

#Learn more :

The angle of elevation of a bird from a point 50 metres above a lake is 30° and the angle of depression of its reflection in the lake is 60°. Find the height of the bird.

https://brainly.in/question/10909974