Law of Cosines, and which law to use

Answer Key - Grade 10 Math Worksheet

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

1. 1.

   Luz's triangle DFG has DF = 8 cm, DG = 13 cm and ∠D = 47° between them. How long is FG, to the nearest tenth?

   9.5
2. 2.

   Milo's triangle DFG has DF = 15 cm, DG = 9 cm and ∠D = 71° between them. How long is FG, to the nearest tenth?

   14.8
3. 3.

   Noah's triangle DFG has DF = 20 cm, DG = 14 cm and ∠D = 33° between them. How long is FG, to the nearest tenth?

   11.2
4. 4.

   Pia's triangle DFG has DF = 6 cm, DG = 10 cm and ∠D = 58° between them. How long is FG, to the nearest tenth?

   8.5
5. 5.

   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?

   73.4
6. 6.

   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?

   59
7. 7.

   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?

   5.5
8. 8.

   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?

   13.4
9. 9.

   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?

   48
10. 10.

    On Kira's map, trails from camp D run 18 km to F and 25 km to G, with 84° between them. How many km is it from F to G, to the nearest tenth?

    29.2