Reading Bearings

Part of the Triangles Without Right Angles section of Coddy's Trigonometry journey. Lesson 28 of 37.

A bearing is an angle measured clockwise from north, written with three digits: 050° is a little east of northeast (045°), 145° a little south of southeast (135°). North lines at different places are parallel, which is what turns two bearings into the angle inside a triangle.

$A course from P on bearing 050° to Q, then on bearing 145° to R, with north lines at P and Q$

A boat sails from P on bearing 050° to Q, then on bearing 145° to R. The north lines at P and Q are parallel, so the angle at Q between north and the way back to P is 180° − 50° = 130° (co-interior angles). Round Q the angles make 360°: 145° + φ + 130° = 360°, so the angle inside the triangle is φ = 85°.

Challenge

A ship sails from P on bearing 060° to Q, then turns onto bearing 170° to R. Find the angle marked ? inside the triangle at Q: tap an angle, pick the reason, and work your way to it. Then press Check.

Try it yourself

$Find the marked part of the figure$