Worksheets · Precalculus

Precalculus law of cosines worksheet

Pythagoras with a correction for the angle not being a right angle. When the angle is 90 degrees the correction vanishes and it becomes Pythagoras exactly.

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Pick more than one for a sheet that mixes them.

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The Law of Cosines

Date Period

Find the missing measure.

  1. In a triangle, c=30, a=51 and B=120∘. Find b
  2. In a triangle, b=33, c=56 and a=65. Find A
  3. In a triangle, b=47, c=70 and A=90∘. Find a
  4. In a triangle, b=32, c=45 and a=67. Find A
  5. In a triangle, a=36, b=50 and C=60∘. Find c
  6. In a triangle, a=11, b=85 and c=91. Find C
  7. In a triangle, b=31, c=47 and A=60∘. Find a
  8. In a triangle, a=33, b=56 and c=65. Find C
  9. In a triangle, a=52, b=61 and C=120∘. Find c
  10. In a triangle, c=33, a=56 and b=65. Find B
  11. In a triangle, a=39, b=61 and C=90∘. Find c
  12. In a triangle, a=35, b=48 and c=43. Find C
  13. In a triangle, a=59, b=53 and C=60∘. Find c
  14. In a triangle, b=13, c=48 and a=43. Find A
  15. In a triangle, c=39, a=70 and B=90∘. Find b
  16. In a triangle, c=17, a=63 and b=73. Find B
  17. In a triangle, c=67, a=58 and B=90∘. Find b
  18. In a triangle, a=48, b=55 and c=73. Find C
  19. In a triangle, c=65, a=42 and B=60∘. Find b
  20. In a triangle, c=11, a=85 and b=91. Find B

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The Law of CosinesAnswer keyVersion 1

Date Period

Find the missing measure.

  1. In a triangle, c=30, a=51 and B=120∘. Find b3559
  2. In a triangle, b=33, c=56 and a=65. Find A90∘
  3. In a triangle, b=47, c=70 and A=90∘. Find a7109
  4. In a triangle, b=32, c=45 and a=67. Find A120∘
  5. In a triangle, a=36, b=50 and C=60∘. Find c2499
  6. In a triangle, a=11, b=85 and c=91. Find C120∘
  7. In a triangle, b=31, c=47 and A=60∘. Find a1713
  8. In a triangle, a=33, b=56 and c=65. Find C90∘
  9. In a triangle, a=52, b=61 and C=120∘. Find c9597
  10. In a triangle, c=33, a=56 and b=65. Find B90∘
  11. In a triangle, a=39, b=61 and C=90∘. Find c5242
  12. In a triangle, a=35, b=48 and c=43. Find C60∘
  13. In a triangle, a=59, b=53 and C=60∘. Find c3163
  14. In a triangle, b=13, c=48 and a=43. Find A60∘
  15. In a triangle, c=39, a=70 and B=90∘. Find b6421
  16. In a triangle, c=17, a=63 and b=73. Find B120∘
  17. In a triangle, c=67, a=58 and B=90∘. Find b7853
  18. In a triangle, a=48, b=55 and c=73. Find C90∘
  19. In a triangle, c=65, a=42 and B=60∘. Find b3259
  20. In a triangle, c=11, a=85 and b=91. Find B120∘

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

In a triangle, a=7, b=5 and C=60∘. Find c

  1. c squared is a squared plus b squared minus 2ab cos C.
  2. 49 plus 25 minus 70 times a half.

The answer is 39.

Where students go wrong

Adding the correction term instead of subtracting it, or using an angle that is not between the two sides. The angle has to sit between them or the rule does not apply.

Also called cosine rule or solving triangles.

What you can put on this worksheet

A missing side, from two sides and the angle between
In a triangle, a=5, b=7 and C=120∘. Find c → 109
A missing angle, from three sides
In a triangle, c=7, a=15 and b=13. Find B → 60∘

Questions about these worksheets

Yes. Every law of cosines sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the law of cosines questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are two levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 2: a missing side, from two sides and the angle between and a missing angle, from three sides. Tick as many as you want and set how many of each, or let it spread them evenly.

Adding the correction term instead of subtracting it, or using an angle that is not between the two sides. The angle has to sit between them or the rule does not apply.