A pilot flying at an altitude of 1.8km sights the runway directly in front of her. The angle of depression to the beginning of the runway is 31 degrees. The angle of depression to the end of the runway is 23 degrees. What is the length of the runway? Round to the nearest tenth of a kilometer.

The distance from the near end of the runway to the plane, divided by the altitude is the tangent of (90 degrees minus the angle of depression). Let "d1" be the distance to the near end of the runway, and "d2" be the distance to the far end of the runway. Let "a" be the altitude of the plane.

d1/a = tan(90 - 31)

d1 = a*tan(90 - 31)

d2/a = tan(90 - 23)

d2 = a*tan(90 - 23)

runway length = d2 - d1 = a*(tan(67) - tan(59))

length = 1800*(.6916) = 1245m = 1.2km

the answer is "a"

ayoushivt ayoushivt · Answer 2 · 2022-06-27T11:27:25+02:00

The length of the runway is 1.24 km.

What is the Angle of Depression ?

The angle made by an observer and the object at a point below the horizontal line on which the observer is standing is called Angle of Depression.

The value of length of runway has to be determined.

The total length of the point at which the observer is standing is given by

1.8 *tan(90-23)

and the length from the observer point on the runway to the beginning of the runway is given by

1.8*tan(90-31)

The difference between the two length is the length of the runway.

1.8*{tan(90-23) - tan(90-31)]}

1.8* { tan(67) - tan(59)}

Approx 1.24 km

The length of the runway is 1.24 km.

To know more about Angle of Depression

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