Topic 3.3: Applications of Trigonometry Questions

The bearing of Q from P is 115°. Find the bearing of P from Q.

The bearing of B from A is 215°. Find the bearing of A from B.

Write down the three-figure bearing of due West.

A ramp rises 2 m over a horizontal distance of 9 m. Find the angle of elevation of the ramp, to 3 s.f.

Express the compass direction N60°W as a three-figure bearing.

From a point 60 m from the foot of a building, the angle of elevation to the top is 38°. Find the height of the building, to 3 s.f.

A kite string of length 40 m makes an angle of elevation of 55° with the ground (string taut and straight). Find the height of the kite above the ground, to 3 s.f.

From the top of a 25 m lighthouse, the angle of depression to a boat is 15°. Find the horizontal distance from the boat to the base of the lighthouse, to 3 s.f.

From a window 1.5 m above the ground, the angle of elevation to the top of a flagpole 20 m away is 28°. Find the total height of the flagpole, to 3 s.f.

A walker goes 6 km on a bearing of 030°, then 10 km on a bearing of 100°. Find the direct distance from the start, to 3 s.f.

Town B is 40 km due East of town A. Town C is 40 km due North of A. Find the bearing of C from B.

Two points A and B are 50 m apart on level ground, in line with the base of a tower. From A the elevation to the top is 35°, and the tower is between... no — from A (nearer) the elevation is 50° and from B (farther) it is 35°. Using the triangle, find the tower height. (Hint: the angle at the top between the two lines of sight is 15°.)

From a cliff top, the angles of depression to two buoys directly out to sea are 30° and 50°. The cliff is 80 m high. Find the distance between the two buoys, to 3 s.f.

A boat sails 12 km on a bearing of 050°, then 9 km on a bearing of 140°. Find its direct distance from the start, to 3 s.f.