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 - Building Confidence

NameDate

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

Luz writes FG² = 7² + 9² − 2 × 7 × 9 × cos 48° for triangle DFG. How long is FG, to the nearest tenth?
Milo writes FG² = 5² + 8² − 2 × 5 × 8 × cos 64° for triangle DFG. How long is FG, to the nearest tenth?
Noah writes FG² = 10² + 12² − 2 × 10 × 12 × cos 38° for triangle DFG. How long is FG, to the nearest tenth?
Pia writes FG² = 6² + 11² − 2 × 6 × 11 × cos 75° for triangle DFG. How long is FG, to the nearest tenth?
5.
Triangle DFG has no right angle: DF = 8, DG = 11 and ∠D = 40°, the angle between them. Ren wants FG. Which rule finds it in one step?
- Law of Sines
- Law of Cosines
- Pythagorean theorem
6.
Triangle DFG has no right angle: DF = 7, DG = 9 and FG = 12. Tala wants ∠D. Which rule finds it in one step?
Use the picture in question 5.
- Law of Cosines
- Law of Sines
- Pythagorean theorem
Bo uses the Law of Cosines on triangle DFG and gets cos D = 11/16. What is ∠D, to the nearest tenth of a degree?
Esme uses the Law of Cosines on triangle DFG and gets cos D = 2/7. What is ∠D, to the nearest tenth of a degree?
Jun uses the Law of Cosines on triangle DFG and gets cos D = 5/7. What is ∠D, to the nearest tenth of a degree?
Kira uses the Law of Cosines on triangle DFG and gets cos D = 13/20. What is ∠D, to the nearest tenth of a degree?

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.

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