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When a 757 passenger jet begins its descent to the Ronald Reagan National Airport in Washington, D.C., it is 3900 feet from the ground. Its angle of descent is 6 degrees

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Answer:

Step-by-step explanation:

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The plane's horizontal distance from the ground is 409.91 ft and the plane must fly 37310.411 ft before it descends to the ground.

Data;

  • Distance of the place from the ground = 3900 ft
  • angle of depression = 6 degree

Trigonometric Ratio

This is a geometric method used to find the side or angle of a right angle triangle.

The plane's ground horizontal distance from the airport

To find the plane's ground distance from the airport, we have to use trigonometric ratio

  • The plane distance from the ground (opposite) = 3900
  • The angle = 6 degree
  • The plane's horizontal distance from the ground (adjacent) = y

From SOHCAHTOA

Using tangent of the angle

[tex]tan \theta = \frac{opposite}{adjacent}\\ tan 6 = \frac{3900}{y}\\ \\y = 37106.02ft[/tex]

The plane's horizontal distance from the ground is 409.91 ft.

How far must the plane fly before it descend to the ground

Using the values above,

Taking the sine angle of this since we have the value of angle and opposite.

[tex]sin\theta = \frac{opposite}{hypothenuse}\\ sin6 = \frac{3900}{x}\\ x = \frac{3900}{sin6}\\ x = 37310.411ft[/tex]

The plane must fly 37310.411 ft before it descends to the ground.

Learn more on trigonometric ratios here;

https://brainly.com/question/10417664

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