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olasank [31]
3 years ago
9

An airplane pilot over the Pacific sights an atoll at an angle of depression of 7 degrees. At this time, the horizontal distance

from the airplane to the atoll is 3,729 meters. What is the height of the plane to the nearest meter?
458 meters
454 meters
3667 meters
3701 meters

I think it's A I'm not sure

Mathematics
2 answers:
svlad2 [7]3 years ago
8 0
It would be helpful if a figure is drawn as you can see clearly the situation of the problem. We would see that a right triangle is made where the angle between the elevation of the airplane with respect to the ground is 7 degrees and the horizontal distance is the base of the triangle. We use trigonemetric functions.

tan 7 = opposite side / adjacent = height / 3729
height = 458 meters
Natali5045456 [20]3 years ago
7 0

Answer: 458 meters

Step-by-step explanation:

Given: The e horizontal distance from the airplane to the atoll = 3,729 meters.

The angle of depression is = 7°

⇒ The angle of elevation from the atoll on ground =7°   [Alternate angle property]

Let h be the height of the plane .

By trigonometry,

\tan x=\frac{\text{side opposite to x}}{\text{side adjacent to x}}\\\Rightarrow\ \tan7^{\circ}=\frac{h}{3729}\\\Rightarrow\ h=3729\times0.122784\\\Rightarrow\ h=457.863\approx458

Thus, the height of the plane to the nearest meter is 458 meters.

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