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In this worksheet, we will practice solving bearings problems using trigonometry.

A boat sails from point A with bearing 1 2 0 ∘ . After the boat sails 10 km , how far south of point A is it?

𝐴 , 𝐵 , and 𝐶 are three ports.

Find the bearing from 𝐶 to 𝐵 .

Find the bearing from 𝐴 to 𝐶 .

Find the bearing from 𝐵 to 𝐴 .

Michael runs east from point O at 4 km/h , and Liam runs south from point O at 10 km/h . After 30 min they stop running; find the bearing that would take Michael to Liam. Round to one decimal place.

𝐴 , 𝐵 , and 𝐶 are three points. The bearing of 𝐴 from 𝐵 is 4 5 ∘ . The bearing of 𝐶 from 𝐴 is 1 3 5 ∘ . If 𝐴 𝐵 = 4 k m and 𝐴 𝐶 = 3 k m , what is the bearing of 𝐵 from 𝐶 to the nearest degree?

Benjamin traveled 12 km to the north and then he traveled 10 km to the east. Find Benjamin’s bearing from his starting point to his end point, to one decimal place.

A boat was spotted 2 miles due south of a lighthouse. It was sailing due east. Some time later, the bearing from the boat to the lighthouse was 3 1 7 ∘ . How far had the boat sailed since it was spotted? Give your answer to two decimal places.

Cities A, B, and C are located such that city A is due west of city B, city C is on a bearing of 3 5 ∘ from city B, and city C is 100 miles from city A and 70 miles from city B. Find the distance between cities A and B giving your answer to one decimal place.

Two boats depart from a dock at the same time. One boat sails at a speed of 18 mph on a bearing of 1 2 3 ∘ , and the other boat sails at a speed of 4 mph on a bearing of 3 0 ∘ . Find the distance between the boats after 2 hours .

An aircraft takes off in search of a submarine. Initially, it is given instructions to fly on a bearing of 0 2 5 ∘ . After 1,250 miles , the aircraft receives new information and changes direction to a bearing of 1 9 7 ∘ . After flying a further 850 miles , the plane detects the submarine. What are the aircraft’s bearing and distance from its original position? Round your distances to the nearest mile, and bearings to two decimal places.

An airplane flies 220 miles on a bearing of 4 0 ∘ and then changes course and flies 180 miles on a bearing of 1 7 0 ∘ . How far is the plane from its starting point and on what bearing? Give your answers to one decimal place.

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(This sheet is a summative worksheet that focuses on deciding when to use the law of sines or cosines as well as on using both formulas to solve for a single triangle's side or angle)

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