To find the bearing from the airplane to the airport, we can use trigonometry.
First, let's draw a diagram to make it easier to understand. Imagine a coordinate system where the airplane is located at point A, and the airport is at point B. The airplane is 120 miles north of the airport, which means point A is located 120 units directly above point B. Similarly, the airplane is 85 miles east of the airport, so point A is located 85 units to the right of point B.
Now, we have a right triangle with sides of 120 and 85 units. We can use the trigonometric function called tangent to find the bearing.
The tangent of an angle is equal to the opposite side divided by the adjacent side. In this case, the angle we are interested in is the angle between the line connecting the airplane and the airport (line AB), and the horizontal axis (x-axis).
The tangent function is defined as: tan(θ) = opposite/adjacent.
To find the bearing, we need to find the angle θ. We can do this by taking the inverse tangent (also known as arctan or tan⁻¹) of the ratio of the opposite side to the adjacent side:
θ = tan⁻¹(120/85)
Using a calculator to evaluate this expression, we find that θ is approximately 55.8 degrees.
Therefore, the bearing from the airplane to the airport is 55.8 degrees (rounded to 1 decimal place).