Question

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

Answer 1

Answer: 458 meters

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)=(h)/(3729)\\\Rightarrow\ h=3729*0.122784\\\Rightarrow\ h=457.863\approx458`

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

Answer 2

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