Bearings with the Law of Cosines

  • 11th Grade
Reviewed by Cierra Henderson
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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Thames
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| Questions: 20 | Updated: Jan 21, 2026
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1) Two planes depart an airport: Plane A flies 260 km on a bearing of 025°, Plane B flies 210 km on a bearing of 080°. How far apart are the planes (nearest km)?

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About This Quiz
Bearings With The Law Of Cosines - Quiz

When two paths or bearings form an angle, how can you find the exact distance between travelers? In this quiz, you’ll use the Law of Cosines to calculate separation distances between planes, ships, and other moving objects. You’ll explore how angles and sides relate in navigation triangles and learn when... see morethis law works best. By the end, you’ll feel confident solving complex bearing problems with accuracy and insight.
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2) A ship sails 320 km on bearing 040°. Another sails 270 km on bearing 115°. Find the distance between them. (round to the nearest whole number)

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3) From the same port, Boat A goes 180 km on 010° and Boat B goes 230 km on 055°. How far apart are the boats? (round to the nearest whole number)

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4) An aircraft flies 240 km on bearing 065°. Another travels 190 km on bearing 130°. How far apart are they? (round to the nearest whole number)

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5) Two cargo planes leave at the same time: A travels 300 km on 030°, B travels 180 km on 095°. Find the separation distance. (round to the nearest whole number)

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6) Ship A sails 210 km on bearing 015°, Ship B sails 260 km on 085°. Find their distance apart. (round to the nearest whole number)

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7) Two helicopters leave base: A flies 170 km on 035°, B flies 210 km on 090°. How far apart are they? (round to the nearest whole number)

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8) A yacht travels 280 km on bearing 050°. Another yacht sails 220 km on 125°. Find the distance between them. (round to the nearest whole number)

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9) Plane A: 160 km on 020°. Plane B: 200 km on 075°. Find their separation. (round to the nearest whole number)

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10) A freighter sails 290 km on 045°, another sails 250 km on 105°. How far apart are they? (round to the nearest whole number)

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11) Two planes are 230 km and 190 km from the airport on bearings 060° and 115°, respectively. If they are 290 km apart, what is the angle between their paths (nearest degree)?

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12) From port, Boat A travels 260 km on bearing 015° and Boat B 240 km on 070°. If their separation is 190 km, what is the approximate angle at the port between their bearings?

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13) Two jets fly 200 km (bearing 055°) and 300 km (bearing 135°). If they are 344 km apart, what approximate angle is formed at the airport between their directions?

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14) Two ships leave port on bearings 010° and 085°, traveling 150 km and 280 km. If they end up 270 km apart, what is the approximate angle between their courses?

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15) From a dock, Boat A sails 240 km on 035°, Boat B sails 260 km on 110°. If they are 360 km apart, find the approximate angle between their bearings.

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16) Two survey aircraft fly 185 km and 215 km on bearings 025° and 095°. If their separation is 260 km, what is the approximate angle at the airport?

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17) A plane on bearing 040° flies 310 km. Another on 120° flies 210 km. They are found to be 400 km apart. What is the approximate angle between their paths?

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18) Two cargo ships depart on bearings 015° (270 km) and 095° (230 km). If they are 340 km apart, what is the included approximate angle between courses?

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19) A patrol boat travels 190 km on bearing 065°, while another goes 260 km on 150°. If they are 350 km apart, find the approximate angle between their bearings.

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20) Two planes fly 220 km (bearing 030°) and 200 km (bearing 105°). If the distance between them is 280 km, what is the approximate angle at the airport?

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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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Two planes depart an airport: Plane A flies 260 km on a bearing of...
A ship sails 320 km on bearing 040°. Another sails 270 km on bearing...
From the same port, Boat A goes 180 km on 010° and Boat B goes 230 km...
An aircraft flies 240 km on bearing 065°. Another travels 190 km on...
Two cargo planes leave at the same time: A travels 300 km on 030°, B...
Ship A sails 210 km on bearing 015°, Ship B sails 260 km on 085°....
Two helicopters leave base: A flies 170 km on 035°, B flies 210 km on...
A yacht travels 280 km on bearing 050°. Another yacht sails 220 km on...
Plane A: 160 km on 020°. Plane B: 200 km on 075°. Find their...
A freighter sails 290 km on 045°, another sails 250 km on 105°. How...
Two planes are 230 km and 190 km from the airport on bearings 060°...
From port, Boat A travels 260 km on bearing 015° and Boat B 240 km on...
Two jets fly 200 km (bearing 055°) and 300 km (bearing 135°). If...
Two ships leave port on bearings 010° and 085°, traveling 150 km and...
From a dock, Boat A sails 240 km on 035°, Boat B sails 260 km on...
Two survey aircraft fly 185 km and 215 km on bearings 025° and 095°....
A plane on bearing 040° flies 310 km. Another on 120° flies 210 km....
Two cargo ships depart on bearings 015° (270 km) and 095° (230 km)....
A patrol boat travels 190 km on bearing 065°, while another goes 260...
Two planes fly 220 km (bearing 030°) and 200 km (bearing 105°). If...
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