20.6 The sine 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 .
- Write the sine ratio for an acute angle .
Answers
- . 2. .
If an answer differs, revisit Section 16.3 for the angle sum in a triangle and Section 20.2 for the sine ratio.
Practise with help
1. In a triangle a=6, A=30°, B=90°. Find b.
Hint
Pair a with A.
Full working
b/sin90° = 6/sin30°, so b = 12.
2. Given a=8, A=30°, B=45°, find b.
Hint
Use the paired sides and angles.
Full working
b = 8 sin45°/sin30° = 8√2.
3. Given a=10, A=90°, b=5, find B.
Hint
Use inverse sine after forming the ratio.
Full working
sin B = 5/10, so B = 30°.
Before opening each full working, name the method and explain which measurements led you to choose it.