Question

An airplane is 105 miles north and 90 miles east of an airport. The pilot wants to fly directly to the airport. What bearing should be taken?

Answer 1

221° from north (to nearest degree)

Explanation:

A bearing is the angle in degrees measured clockwise from north.

Bearings are usually given as a three-figure bearing. For example, 30° clockwise from north is usually written as 030°.

So we need to calculate the angle shown on the attached diagram.

To do this, use trig ratios to find the smallest angle of the right triangle, then add this to 180.

tan(x)=O/A=90/105

⇒ x = arctan(90/105) = 40.601294...°

Therefore, bearing = 180 + 40.601294...° = 221° (to nearest degree)