Law of Cosines, and which law to use

Answer Key - Grade 10 Math Worksheet - Building Confidence

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

1. 1.

   Milo writes FG² = 5² + 8² − 2 × 5 × 8 × cos 64° for triangle DFG. How long is FG, to the nearest tenth?

   7.3
2. 2.

   Noah writes FG² = 10² + 12² − 2 × 10 × 12 × cos 38° for triangle DFG. How long is FG, to the nearest tenth?

   7.4
3. 3.

   Pia writes FG² = 6² + 11² − 2 × 6 × 11 × cos 75° for triangle DFG. How long is FG, to the nearest tenth?

   11.1
5. 4.

   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. 5.

   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 4.

   • Law of Sines
   • Law of Cosines
   • Pythagorean theorem
7. 6.

   Triangle DFG has no right angle: ∠D = 52°, ∠F = 71° and DG = 10, across from ∠F. Zee wants FG. Which rule finds it in one step?

   Use the picture in question 4.

   • Law of Cosines
   • Law of Sines
   • Pythagorean theorem
8. 7.

   Triangle DFG has no right angle: DF = 15 between ∠D = 38° and ∠F = 64°. Ari wants FG. Which rule finds it in one step?

   Use the picture in question 4.

   • Pythagorean theorem
   • Law of Sines
   • Law of Cosines
9. 8.

   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?

   46.6
10. 9.

    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?

    73.4
11. 10.

    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?

    44.4