Worksheets · Precalculus

Precalculus law of sines worksheet

Each side over the sine of the angle opposite it gives the same number. Use it when you have a side and the angle across from it.

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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 Sines

Date Period

Find the missing measure.

  1. In a triangle, A=45∘, C=105∘ and a=27 ext.FindthesideoppositeB
  2. In a triangle, A=45∘, C=105∘ and a=55 ext.FindthesideoppositeB
  3. In a triangle, A=120∘, C=30∘ and a=35 ext.FindthesideoppositeB
  4. In a triangle, A=45∘, C=105∘ and a=47 ext.FindthesideoppositeB
  5. In a triangle, A=30∘, C=90∘ and a=55 ext.FindthesideoppositeB
  6. In a triangle, A=30∘, C=90∘ and a=41 ext.FindthesideoppositeB
  7. In a triangle, A=30∘, C=105∘ and a=38 ext.FindthesideoppositeB
  8. In a triangle, A=45∘, C=75∘ and a=31 ext.FindthesideoppositeB
  9. In a triangle, A=30∘, C=90∘ and a=28 ext.FindthesideoppositeB
  10. In a triangle, A=30∘, C=90∘ and a=49 ext.FindthesideoppositeB
  11. In a triangle, A=45∘, C=75∘ and a=32 ext.FindthesideoppositeB
  12. In a triangle, A=30∘, C=105∘ and a=39 ext.FindthesideoppositeB
  13. In a triangle, A=45∘, C=105∘ and a=50 ext.FindthesideoppositeB
  14. In a triangle, A=45∘, C=105∘ and a=42 ext.FindthesideoppositeB
  15. In a triangle, A=60∘, C=75∘ and a=32 ext.FindthesideoppositeB
  16. In a triangle, A=60∘, C=75∘ and a=40 ext.FindthesideoppositeB
  17. In a triangle, A=60∘, C=75∘ and a=55 ext.FindthesideoppositeB
  18. In a triangle, A=45∘, C=75∘ and a=48 ext.FindthesideoppositeB
  19. In a triangle, A=30∘, C=105∘ and a=36 ext.FindthesideoppositeB
  20. In a triangle, A=30∘, C=90∘ and a=34 ext.FindthesideoppositeB

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

Sigma Prep · sigmaprep.io/worksheets

Name

The Law of SinesAnswer keyVersion 1

Date Period

Find the missing measure.

  1. In a triangle, A=45∘, C=105∘ and a=27 ext.FindthesideoppositeB2722
  2. In a triangle, A=45∘, C=105∘ and a=55 ext.FindthesideoppositeB5522
  3. In a triangle, A=120∘, C=30∘ and a=35 ext.FindthesideoppositeB3533
  4. In a triangle, A=45∘, C=105∘ and a=47 ext.FindthesideoppositeB4722
  5. In a triangle, A=30∘, C=90∘ and a=55 ext.FindthesideoppositeB553
  6. In a triangle, A=30∘, C=90∘ and a=41 ext.FindthesideoppositeB413
  7. In a triangle, A=30∘, C=105∘ and a=38 ext.FindthesideoppositeB382
  8. In a triangle, A=45∘, C=75∘ and a=31 ext.FindthesideoppositeB3162
  9. In a triangle, A=30∘, C=90∘ and a=28 ext.FindthesideoppositeB283
  10. In a triangle, A=30∘, C=90∘ and a=49 ext.FindthesideoppositeB493
  11. In a triangle, A=45∘, C=75∘ and a=32 ext.FindthesideoppositeB166
  12. In a triangle, A=30∘, C=105∘ and a=39 ext.FindthesideoppositeB392
  13. In a triangle, A=45∘, C=105∘ and a=50 ext.FindthesideoppositeB252
  14. In a triangle, A=45∘, C=105∘ and a=42 ext.FindthesideoppositeB212
  15. In a triangle, A=60∘, C=75∘ and a=32 ext.FindthesideoppositeB3263
  16. In a triangle, A=60∘, C=75∘ and a=40 ext.FindthesideoppositeB4063
  17. In a triangle, A=60∘, C=75∘ and a=55 ext.FindthesideoppositeB5563
  18. In a triangle, A=45∘, C=75∘ and a=48 ext.FindthesideoppositeB246
  19. In a triangle, A=30∘, C=105∘ and a=36 ext.FindthesideoppositeB362
  20. In a triangle, A=30∘, C=90∘ and a=34 ext.FindthesideoppositeB343

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

How to do these

In a triangle, A=30∘, B=45∘ and a=8. Find b

  1. a over sin A equals b over sin B.
  2. So b is a sin B over sin A.

The answer is 8sin⁡45∘sin⁡30∘.

Where students go wrong

Pairing a side with the wrong angle. The rule only works when the angle is opposite the side, not merely next to it.

Also called sine rule or solving oblique triangles.

Questions about these worksheets

Yes. Every law of sines 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 sines 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.

Pairing a side with the wrong angle. The rule only works when the angle is opposite the side, not merely next to it.