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(ii) A peacock is sitting on the tree and observes its prey on
the ground. It makes an angle of depression of 22° to
catch the prey. The speed of the peacock was observed to
be 10 km/hr and it catches its prey in 1 min 12 seconds.
At what height was the peacock on the tree?
(cos 22° = 0.927, sin 22° = 0.374, tan 22° = 0.404)
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Respuesta :

lublana

Answer:

74.8 m

Step-by-step explanation:

We are given that

[tex]\theta=22^{\circ}[/tex]

Speed of peacock,v=10 km/h

Time,t=1 min 12 sec=60+12=72 s=[tex]\frac{72}{3600}=0.02 h[/tex]

1 hour=3600 s

Distance=vt=[tex]10\times 0.02=0.2 km=0.2\times 1000=200 m[/tex]

Using 1 km=1000 m

We know that

[tex]sin\theta=\frac{Perpendicular\;side}{hypotenuse}[/tex]

Using the formula

[tex]sin22=\frac{h}{200}[/tex]

[tex]h=200sin22=200\times 0.374=74.8 m[/tex]

Hence, the peacock was at height  of 74.8 m on the tree.

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