Bearings with the Law of Sines

  • 10th Grade
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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 11 | Questions: 20 | Updated: Dec 10, 2025
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1) Starting from a lighthouse, a boat motors 200 km on bearing 020°, then shifts to bearing 110° and goes 250 km further. What is the boat's distance from the lighthouse? (round to the nearest whole number)
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About This Quiz
Bearings With The Law Of Sines - Quiz

Ever wonder how ships and planes find their exact positions using angles and distances? In this quiz, you’ll apply the Law of Sines to solve real-world navigation problems involving bearings. You’ll calculate unknown distances, interpret course changes, and understand how triangles model movement across directions. Step by step, you’ll see... see morehow trigonometry helps navigators stay precise — even miles out at sea!
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2) A patrol boat travels 15 km on bearing 090°, then 25 km on bearing 180°. The angle between the two legs of the journey is closest to which value?
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3) A cruise ship leaves port on a 045° bearing, covering 50 km. It then pivots to 135° and sails 70 km. Determine the direct route distance back to port. (round to the nearest whole number)
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4) A submarine surfaces and travels 180 km at 060°, then submerges and moves 200 km at 150°. What is its net displacement from the starting location? (round to the nearest whole number)
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5) From its home base, a coast guard cutter proceeds 35 km on course 030°, then alters course to 120° for 40 km. How far is it from base? (round to the nearest whole number)
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6) A freighter sails 300 km on bearing 045°, then 400 km on bearing 13 5°. What is the angle formed at the turning point between the two course segments?
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7) A tanker exits the harbor at bearing 045° and travels 15 km, then redirects to 135° for 25 km. Find the shortest distance to return to harbor. (round to the nearest whole number)
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8) A research vessel navigates 80 km at 030° from its dock, then changes heading to 120° and continues 100 km. Calculate the linear distance from the dock. (round to the nearest whole number)
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9) Leaving an island, a sailboat tracks 50 km on 060°, then 60 km on 150°. What is the straight-line distance back to the island? (round to the nearest whole number)
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10) A ship travels 120 km on bearing 020°, then 150 km on bearing 110°. The navigation triangle's angle at the starting point is approximately:
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11) A ferry departs on bearing 045° and covers 200 km, then switches to 135° for another 250 km. How far is the ferry from its departure point (nearest km)?
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12) An oil tanker moves 75 km on heading 030°, then modifies its course to 120° and proceeds 80 km. What is the displacement from origin? (round to the nearest whole number)
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13) A speedboat races 20 km at bearing 060°, then turns to 150° and continues for 25 km. Find the direct distance to the starting line. (round to the nearest whole number)
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14) Two legs of a ship's journey are 150 km at 045° and 200 km at 135°. What angle do these bearings create? (round to the nearest whole number)
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15) A container ship steams 40 km on 030° bearing, then adjusts to 120° and travels 50 km more. Calculate the crow-fly distance back to port. (round to the nearest whole number)
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16) A catamaran sets out from shore, traveling 100 km along bearing 060°, followed by 120 km on bearing 150°. Determine its distance from shore. (round to the nearest whole number)
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17) A cargo ship departs from harbor on a bearing of 045°. After sailing 15 km, the captain changes course to 120° and travels 20 km more. What is the ship's straight-line distance from the harbor? (round to the nearest whole number)
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18) A fishing vessel leaves port traveling 120 km on bearing 030°, then changes direction to bearing 120° for 150 km. How far is the vessel from its starting point (nearest km)?
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19) A yacht sails 40 km on a heading of 070°, then adjusts to 160° for an additional 60 km. Find the direct distance back to the starting point. (round to the nearest whole number)
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20) A naval destroyer travels 25 km at bearing 045° before turning to bearing 135° and continuing for 30 km. Calculate its displacement from the original position. (round to the nearest whole number)
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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Starting from a lighthouse, a boat motors 200 km on bearing 020°,...
A patrol boat travels 15 km on bearing 090°, then 25 km on bearing...
A cruise ship leaves port on a 045° bearing, covering 50 km. It then...
A submarine surfaces and travels 180 km at 060°, then submerges and...
From its home base, a coast guard cutter proceeds 35 km on course...
A freighter sails 300 km on bearing 045°, then 400 km on bearing 13...
A tanker exits the harbor at bearing 045° and travels 15 km, then...
A research vessel navigates 80 km at 030° from its dock, then changes...
Leaving an island, a sailboat tracks 50 km on 060°, then 60 km on...
A ship travels 120 km on bearing 020°, then 150 km on bearing...
A ferry departs on bearing 045° and covers 200 km, then switches to...
An oil tanker moves 75 km on heading 030°, then modifies its course...
A speedboat races 20 km at bearing 060°, then turns to 150° and...
Two legs of a ship's journey are 150 km at 045° and 200 km at 135°....
A container ship steams 40 km on 030° bearing, then adjusts to 120°...
A catamaran sets out from shore, traveling 100 km along bearing...
A cargo ship departs from harbor on a bearing of 045°. After...
A fishing vessel leaves port traveling 120 km on bearing 030°, then...
A yacht sails 40 km on a heading of 070°, then adjusts to 160° for...
A naval destroyer travels 25 km at bearing 045° before turning to...
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