Question

The air traffic control tower in Dublin, Ireland is 87.7 meters tall. If someone
in the tower (assume they are at the top even though they would actually be
slightly lower) measures the angle of inclination to a plane to be 17.4 degrees
and the pilot communicates that the plane is currently flying at an altitude of
715 meters, how far away from the tower is the plane?

Answer 1

The distance from the tower to the plane is approximately 2014 meters.

The situation forms a right angle triangle. Therefore,

Characteristics of a right angle:

• One of it angle is equals to 90 degree.

• The sides and the angle can be found using trigonometric ratios.

The height of the triangle is the plane altitude - traffic tower height which is 715 - 87.7 = 627.3 meters.

The angle of inclination from the tower to the plane is given as 17.4 degrees.

The distance from the tower to the plane is the adjacent side of the triangle. Therefore,

tan 17.4 = opposite / adjacent

tan 17.4 = 627.3 / a

a = 627.3 / tan 17.3

a = 627.3 / 0.31146531595

a = 2014.02842586

a = 2014 meters.

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