Answer:
124.2 miles
∠310.1°
Explanation:
You want to know the bearing and distance to the airport from a plane that is 95 miles east and 80 miles south of it.
Distance
The Pythagorean theorem or the distance formula can be used to find the distance to the airport.
d = √((x2 -x1)² +(y2 -y1)²)
d = √((95 -0)² +(-80 -0)²) = √(9025 +6400) = √15425
d ≈ 124.197 . . . . miles
The plane is about 124.2 miles from the airport.
Bearing
The reference angle with respect to the +y axis can be found using the tangent relation.
Tan = Opposite/Adjacent
tan(α) = 95/80 = 19/16
α = arctan(19/16) ≈ 49.9° . . . . . . CCW from +y axis
The bearing angle is measured clockwise from the +y axis (north), so is ...
bearing = 360° -49.9° = 310.1°
The bearing to the airport is 310.1°.
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Additional comment
Some navigators would refer to the bearing as N 49.9° W.
Less commonly, it might be referred to as W 40.1° N. Usually, N and S are the reference directions, with the modification being E or W from there. The less common usage might be chosen if an angle less than 45° is wanted.
The bearing is often reported to the nearest degree, without any degree symbol, as N50W.