Question

A passenger is travelling in an airplane. An airplane is
flying at a height of 3000 m above the level ground. He observes that the angle of depression
from the plane to the foot of a tree is a, such that cos3a = sin(120° - 4a). Find the distance that
the airplane must fly to be directly above the tree.​

Answer 1

Answer:

5190m

Step-by-step explanation:

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Answer 2

The distance that  the airplane must fly to be directly above the tree. is 5196 m (approximately)

Step-by-step explanation:

here , from the figure given

$\tan\alpha = \sin(120-4\alpha )\\\\\sin (90-3\alpha ) = \sin (120-4\alpha)\\\\90-3\alpha=120-4\alpha\\\\4\alpha-3\alpha=120-90\\\\\alpha=30^\circ$

then in triangle ABC

$\tan\alpha = \frac{AB}{BC}\\\\\tan\alpha =\frac{3000}{x}\\\\\tan 30 = \frac{3000}{x}\\\\\frac{1}{\sqrt{3}}=\frac{3000}{x}\\\\x= 3000\sqrt{3}\\\\\sqrt{3}= 1.732..\\\\x= 3000\times 1.732\\\\x=5196 m$

hence , The required distance is 5196 m

#Learn more:

The angle of elevation of an airplane from a point on the ground is 600. After a flight of  30 seconds, the angle of elevation becomes 300. If the airplane is flying at a constant  height of 3000√3 m, find the speed of the airplane.

https://brainly.in/question/15895040