A peacock is sitting on the top of a tree It observes a serpent on the ground making an - Maths - Some Applications of Trigonometry

Question

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

Ajanta Trivedi · Accepted Answer

let AB be the height of the tree, such that AB=h m.

and peacock is sitting at the point A and the serpent is at the point C.

the angle of depression is ∠PAC=∠ACB=30 deg

the speed of peacock =300 m/min, it catches the serpent in 12 seconds

distance travelled by peacock in 12 seconds= $300 * \frac{12}{60} = 60 m .$

i.e. the distance between the peacock and the serpent. therefore AC=60 m.

in the right angled triangle ABC

$\sin 30 = \frac{A B}{A C} \frac{1}{2} = \frac{h}{60} \Rightarrow h = \frac{60}{2} = 30 m .$

hence the height of the tree is 30 m.

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