20.7 The cosine rule — Practise with help
Try each problem first. Open a hint if you need it, then use the working to check your method.
Warm-up: remember
Answer these from memory. Do not look back at the section.
- Work out .
- Make the subject of .
Answers
- . 2. .
If an answer differs, revisit Section 3.2 for square roots and Section 8.6 for rearranging formulae.
Practise with help
1. Two sides 3 and 4 include 90°. Find the third side.
Hint
Use the cosine rule with the included angle.
Full working
c² = 3² + 4² − 24 cos90° = 25, so c = 5.
2. Sides 5 and 6 include 60°. Find opposite side.
Hint
Substitute the included angle.
Full working
c² = 25 + 36 − 60 cos60° = 31; c = √31.
3. Sides 4, 5, 6. Find the angle opposite 6.
Hint
Rearrange cosine rule for cos C.
Full working
cos C = (16+25−36)/40 = 1/8; C ≈ 82.8°.
Before opening each full working, name the method and explain which measurements led you to choose it.