Bearings in Multi-Leg Journeys

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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) A ship goes 50 km on a bearing of 060°, then 70 km on a bearing of 140°. Which side of the triangle represents total displacement?
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Bearings In Multi-leg Journeys - Quiz

What happens when a traveler changes direction multiple times? In this quiz, you’ll solve multi-leg bearing problems using trigonometric laws to find straight-line distances. You’ll apply the Law of Cosines and Law of Sines to determine total displacement after several turns. Each scenario helps you understand how navigators piece togethe... see moreroutes from bearings and distances — and calculate exactly how far they’ve really gone!
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2) A boat sails 25 km at a bearing of 045°, then 30 km at a bearing of 135°. How far is it from the start (nearest km)?
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3) A plane flies 200 km on a bearing of 020°, then 250 km on a bearing of 110°. Which formula applies to find its distance from the start?
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4) Two planes leave an airport: one flies 150 km on a bearing of 030°, the other 200 km on a bearing of 120°. How far apart are they?
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5) A boat sails 100 km on a bearing of 060°, then 120 km on a bearing of 150°. What is its displacement?
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6) Which triangle case do multi-leg bearing problems usually form?
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7) Why can’t the Pythagorean Theorem usually be applied in bearings problems?
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8) A boat sails 15 km on a bearing of 070°, then 20 km on a bearing of 160°. To find the straight-line distance from its starting point, which law is most efficient?
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9) A hiker travels 8 km due north, then 6 km on a bearing of 120°. What information is needed to apply the Law of Cosines?
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10) A ship travels 10 km on a bearing of 045°, then 12 km on a bearing of 135°. Which triangle type is formed when computing displacement?
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11) In multi-leg bearing problems, why is the Law of Cosines often preferred over the Law of Sines?
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12) A plane flies 100 km on a bearing of 030°, then 120 km on a bearing of 120°. How far is it from its start (nearest km)?
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13) A car travels 40 km due east, then 30 km on a bearing of 150°. Which law helps find the straight-line distance back to the start?
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14) A cyclist travels 15 km east, then 20 km at a bearing of 120°. What’s the best method to find the displacement?
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15) In bearings problems, what is typically the known angle when applying the Law of Cosines?
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16) A ship goes 60 km at a bearing of 090°, then 80 km at a bearing of 180°. How far is it from port (nearest km)?
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17) A hiker walks 12 km at a bearing of 045°, then 15 km at a bearing of 135°. Which law should be used?
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18) A plane flies 80 km at a bearing of 045°, then 100 km at 135°. What is its displacement (nearest km)?
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19) A ship goes 40 km at a bearing of 010°, then 50 km at a bearing of 100°. How far is it from port (nearest km)?
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20) In multi-leg journeys, which of the following is essential before applying the Law of Cosines?
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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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A ship goes 50 km on a bearing of 060°, then 70 km on a bearing of...
A boat sails 25 km at a bearing of 045°, then 30 km at a bearing...
A plane flies 200 km on a bearing of 020°, then 250 km on a bearing...
Two planes leave an airport: one flies 150 km on a bearing of...
A boat sails 100 km on a bearing of 060°, then 120 km on a bearing...
Which triangle case do multi-leg bearing problems usually form?
Why can’t the Pythagorean Theorem usually be applied in bearings...
A boat sails 15 km on a bearing of 070°, then 20 km on a bearing...
A hiker travels 8 km due north, then 6 km on a bearing of 120°. What...
A ship travels 10 km on a bearing of 045°, then 12 km on a bearing of...
In multi-leg bearing problems, why is the Law of Cosines often...
A plane flies 100 km on a bearing of 030°, then 120 km on a...
A car travels 40 km due east, then 30 km on a bearing of 150°. Which...
A cyclist travels 15 km east, then 20 km at a bearing of 120°....
In bearings problems, what is typically the known angle when applying...
A ship goes 60 km at a bearing of 090°, then 80 km at a bearing of...
A hiker walks 12 km at a bearing of 045°, then 15 km at a bearing of...
A plane flies 80 km at a bearing of 045°, then 100 km at 135°....
A ship goes 40 km at a bearing of 010°, then 50 km at a bearing of...
In multi-leg journeys, which of the following is essential before...
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