Grade 10 · Math · Geometry

10th grade Law of Cosines, and which law to use worksheet

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Law of Cosines, and which law to use

Grade 10 Math Worksheet

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Circle the best answer, or write your answer on the line.

Luz's triangle DFG has DF = 8 cm, DG = 13 cm and ∠D = 47° between them. How long is FG, to the nearest tenth?
Milo's triangle DFG has DF = 15 cm, DG = 9 cm and ∠D = 71° between them. How long is FG, to the nearest tenth?
Noah's triangle DFG has DF = 20 cm, DG = 14 cm and ∠D = 33° between them. How long is FG, to the nearest tenth?
Pia's triangle DFG has DF = 6 cm, DG = 10 cm and ∠D = 58° between them. How long is FG, to the nearest tenth?
Ren's triangle DFG has DF = 7 cm, DG = 8 cm and FG = 9 cm. What is ∠D, to the nearest tenth of a degree?
Zee's triangle DFG has DF = 13 cm, DG = 15 cm and FG = 14 cm. What is ∠D, to the nearest tenth of a degree?
Ari's triangle DFG has DF = 9 cm, DG = 11 cm and FG = 10 cm. What is ∠D, to the nearest tenth of a degree?
Bo watches two boats leave dock D: one sails 4 km to F, the other 7 km to G, with 52° between their paths. How many km apart are they, to the nearest tenth?
Esme's garden fences DF = 9 m and DG = 12 m meet at ∠D = 78°. A third fence will join F and G. How long is it, to the nearest tenth?
Jun holds two kite strings at D: 35 m to kite F and 50 m to kite G, with 66° between them. How far apart are the kites, to the nearest tenth?

The Law of Cosines. Every version has 10 questions, and the answer key prints on the second page.

Standard: G-SRT.D.10 (+), G-SRT.D.11 (+)

included angle: The angle between two given sides, where they meet.

Law of Cosines: FG² = DF² + DG² − 2 × DF × DG × cos D.

SAS, SSS: Two sides and the angle between them; three sides.

side-angle pair: A side and the angle across from it, both known (needed for Sines).

Your child added the 2ab cos part instead of subtracting it.

Your child stopped at the square of the side.

Your child left the 2 out of 2ab cos C.

Ask: what sign comes before the 2 in the Law of Cosines?

Ask: is that the side or the side squared?

Ask: how many times does the cosine part get counted?

What is the most common mistake with law of cosines, and which law to use?

Your child added the 2ab cos part instead of subtracting it.

How can I help my child with law of cosines, and which law to use?

Ask: what sign comes before the 2 in the Law of Cosines?

Are these 10th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records