In order to safely land, the angle that a plane approaches the runway should be no more than 15°. A plane is approaching Ottawa Macdonald–Cartier International Airport to land. It is at an altitude of 500 m and a horizontal distance of 3 km from the start of the runway. At what angle is the plane approaching and is it safe for the plane to land?

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  9.5°, yes

Step-by-step explanation:

The relevant trig relation is ...

  Tan = Opposite/Adjacent

The distance opposite the angle of elevation is the plane's height, 500 m. The distance adjacent to the angle of elevation is the horizontal distance to the plane, 3 km = 3000 m. Then the angle is found from ...

  tan(α) = 500/3000 = 1/6

  α = arctan(1/6) ≈ 9.46°

The plane is approaching at an angle of 9.46°. It is safe to land, since that angle is less than 15°.

Additional comment

The usual descent angle for most commercial air traffic is 3°. Some airport geography demands it be different (steeper). A higher descent angle can put undue stress on the landing gear.

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