Watch out
Pairing a side with the wrong angle.
Scottish National 5 Mathematics
National 5 Maths Sine rule
Use the sine rule to find a missing side or angle from matching side-angle pairs.
Formula reference
Check the National 5 rules and formulae linked to this topic.
Which method?
Match exam clues to a suitable method.
Before you start
- Check the triangle is not right-angled.
- Look for a matching side-angle pair.
- Decide whether you are finding a side or an angle.
Explanation
The sine rule is used in non-right-angled triangles when you have a matching side and opposite angle pair.
Use = when finding a side, or = when finding an angle.
Angles and their opposite sides must match across the triangle.
Visual support
Sine rule pairs
Key formulae and rules
- = =
- =
Check
Match each side with its opposite angle and check that the largest side is opposite the largest angle.
Exam tip
Circle a known matching pair before writing the sine rule.
Calculator tip
Use degree mode and keep full calculator values until the final requested rounding.
Worked examples
Worked example 1
Find a side
In triangle ABC, A = 40°, B = 65° and side a = 8 cm. Find side b
- Use b / sin 65 = 8 / sin 40.
- b = 8 sin 65 / sin 40
- b = 11.28..
Answer: b = 11.3 cm to 1 decimal place
Worked example 2
Find an angle
In triangle ABC, a = 7 cm, b = 10 cm and A = 35°. Find angle B
- = sin
- sin B = 10 sin
- B = sin−1(0.819...)
So: B = 55.0° to 1 decimal place
Worked example 3
Find a third angle first
A = 50°, C = 80°, side a = 12 cm. Find side c.
- A and side a form a matching pair.
- c / sin 80 = 12 / sin 50
- c = 12 sin 80 / sin 50
Answer: c = 15.4 cm to 1 decimal place
Watch out
- Pairing a side with the wrong angle.
- Using sine rule when there is no matching pair.
- Rounding an angle before using it again.