Question Type 2: Exploring complex formulations using bearings and angles Exercises

Points A and B have coordinates A(2, 1) and B(8, 5). Calculate the bearing of B from A to the nearest degree.

A ship travels from P to Q on a bearing of 145° for 35 km. Find the coordinates of Q if P is at (10, −5), using north as the positive y-axis and east as the positive x-axis. Round your answers to one decimal place.

Three survey points A, B and C form a triangle. The bearing of B from A is 045°, and the bearing of C from A is 120°. Given AB=5 km and AC=7 km, calculate the angle at A in the triangle ABC.

From a lighthouse at L, bearings to two ships A and B are 060° and 150° respectively. If the ships are each 20 km from L, calculate the distance AB.

A patrol boat moves from P to Q on bearing 135° for 25 km, then to R on bearing 015° for 30 km. Determine the bearing of R from P.

From point M, the bearings of two landmarks C and D are 012° and 270° respectively. If MC=12 km and MD=8 km, find the distance CD to the nearest kilometre.

A plane travels from R to S on a bearing of 315° for 120 km, then turns through 150° clockwise and flies 80 km to T. Find the bearing of T from R.

An aircraft flies from D to E on a bearing of 220° for 150 km, then turns onto a bearing of 030° and flies a further 180 km to F. Calculate the straight-line distance DF, giving your answer to the nearest kilometre.

Stations A and B are 40 km apart on a due east-west line (B east of A). A ship S is such that its bearing from A is 060° and from B is 330°. Determine the distance AS.

From station X, an aircraft is sighted on a bearing of 070° at 50 km. Another station Y, 30 km due east of X, observes the same aircraft on a bearing of 310°. Determine the position of the aircraft relative to X by coordinates (x, y).

A navigator at N hears two bearings to a drifting buoy: 200° and, after moving 15 km due north, 230°. Find the position of the buoy relative to the initial point N.

An airplane departs Q, flies 200 km on a bearing of 350°, then flies 150 km on a bearing of 260°, and finally returns directly to Q. Calculate the bearing of this return leg.