Question

please tell me the step by step solution or do it on a notebook and snd the photo.​

Answer 1

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Refer to the attachment ⬆️☺❄☺

Answer 2

Question:-

A peacock it sitting on the top of a tree. It observes serpent on the ground making an angle of depression 30°. The peacock with the speed of 300 m/minute catches the serpent in 12 seconds. What is the height of the tree?

Given:-

a) A peacock it sitting on the top of a tree. It observes serpent on the ground making an angle of depression 30°.

b) The peacock with the speed of 300 m/minute catches the serpent in 12 seconds.

Find:- The height of the tree?

Solution:-

{According to figure}

let position of peacock is A and AB is height of tree from base, mean's tree perpendicular to its base. let, position of peacock is A from base B and angle of depression is angle DAC.

First we need to find the speed of peacock in meter/second .

so now { from given ( b ) }

=> 300 m/minute = {300/60} m/s

=> 300 m/minute = 5 m/s ...... ( 1 )

{ from given ( b ) }

The peacock catches the serpent in 12 seconds.

mean's {from ( 1 )} peacock cover

12 × 5 m distance .

Now, distance cover by pecock in 12 seconds = 12 × 5 = 60 m ..... ( 1 )

{According to given & figure & ( 1 )}

position of serpent ( C ) 60 m away from peacock ( A )

Hence, AC = 60 m ...... ( 2 )

According to figure and given angle of depression is 30° which is alternate to angle ACB mean's angle ACB = 30° {alternate angle property}

To find height of tree we use sin ratio.

{ According to figure } position of pecock ( A ) , tree (AB) & serpent ( C ) are make an right angle triangle, so

=> AB = hypotenuse

now According to sin ratio & figure { we theta = 30° }

=> sin (theta)

= (opposite side)/(hypotenuse)

=> sin (theta) = ( AB )/(AC)

=> sin 30° = ( AB )/( 60 )

{ we know sin 30° = 1/2 }

=> 1/2 = ( AB )/(60) i.e.

=> AB = 60/2

=> AB = 30 m ...... ( 3 )

we know AB is height of tree.

Hence { From ( 3 ) }

Height of tree is 30 m.

i hope it helps you.