Curriculum
Pure Mathematics — Second Secondary
Unit 1: Real Functions and Curve Sketching
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Unit 2: Exponents and Logarithms
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Unit 3: Limits
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Text lesson
The Sine Rule
The Sine Rule
The ambiguous case
The ambiguous case
- Suppose we know the sides a and b and the angle A opposite to a, where A is not between the two sides.
- From the rule, sin B = b sin A / a.
- There may be two possibilities:
| Condition | Number of triangles |
|---|---|
| b sin A > a | No triangle |
| b sin A = a | One triangle, right-angled at B |
| a ≥ b | Exactly one triangle |
| a < b and b sin A < a |
|
- When there are two triangles
- we check that the sum of the two known angles is less than 180° for each value of B
- so that the third angle C is positive.
The Sine Rule · 2 / 5