Question

The angle of elevation of a bird from a point 50 meters above a lake is 30 degree and the angle...

Answer 1

HELLO DEAR,

your i think your question is incomplete,

then questions is----------> the angle of elevation of a bird from a point 50m above a lake is 30degree and angle of depression of its reflection in the lake is 60degree find the height of bird above the lake

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

which is at a height of 60m above the lake BE .

Let the height of the bird from the surface of the lake be CE = h metres

the reflection of bird in the lake F will be at the same distance ‘h’ metres from the surface of the lake.

Let AD = BE = x metres

AB = 50 m

=> CD = (h – 50) m

In right ΔADC, θ = 30°

$\bold{ \tan(30) = \frac{cd}{ad} } \\ \bold{ = > \frac{1}{ \sqrt{3} } = \frac{h - 50}{x} }\\ \bold{= > x = \sqrt{3} h - 50 \sqrt{3} ........(1)}$

In right ΔADF, θ = 60°

$\bold{\tan(60 ) = \frac{df}{ad} } \\ \bold{ = > \sqrt{3} = \frac{h}{x} .......(2)} \\ \bold{= > \frac{h}{ \sqrt{3} } = \sqrt{3} h - 50 \sqrt{3} ..using \: \: .....(1) }\\ \bold{ = > h = 3h - 50 \times 3} \\ \bold{ = > 2h = 150 }\\ \\ \bold{= > h = \frac{150}{2}} \\ \bold{ = > h = 75m}$

the height of the bird from the surface of the lake is 75 metres.

I HOPE ITS HELP YOU DEAR,

THANKS

Answer 2

it's correct method and correct answer.