20.7 The cosine rule — Practise

Work independently. Estimate where useful, show your method, and check units. In the mixed questions, choose the method and give a reason.

1. H Two sides are 5 cm and 7 cm with included angle 60°. Find the third side exactly.
2. H Two sides are 6 cm and 8 cm with included angle 90°. Find the third side.
3. H A triangle has sides 5 cm, 6 cm and 8 cm. Find the angle opposite side 8 to 1 decimal place.
4. H Two sides are 10 cm and 12 cm with included angle 30°. Find the opposite side to 1 decimal place.
5. H Two sides are 7 cm and 9 cm with included angle 120°. Find the third side to 1 decimal place.
6. H A triangle has sides 4 cm, 5 cm and 6 cm. Find the angle opposite side 6 to 1 decimal place.
7. H Two sides are 8 cm and 11 cm with included angle 75°. Find the third side to 1 decimal place.
8. H A triangle has sides 9 cm, 10 cm and 13 cm. Find its largest angle to 1 decimal place.