LEARN · EXPLAIN · REVISE

Explain why the sine rule in an SSA problem may give two triangles.

Read the idea, work independently, then explain what changed.

高一必修第二册(A版).pdf · 6.4 · PDF 45 / printed page 38

TOPIC 01

Applications of plane vectors

Build understanding of applications of plane vectors through definitions, contrasting cases and justified applications.

Use one hint at a time. A correction explains what changed, not just the final answer.

01 / Transfer#Worked example

\sin B=s,\quad0<s<1

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Translate the geometry or physical quantity into vectors and check angle conventions.

Hint 2

The inverse sine calculator gives only a principal angle.

Worked solution

Translate the geometry or physical quantity into vectors and check angle conventions.
Calculate or simplify this relation.
$\sin B=\sin(180^{\circ}-B)$
A supplementary candidate is discarded if the angle sum makes it impossible.

Both B and 180°−B have the same sine; each must be checked against the remaining angle and side conditions.

Checks and common pitfalls: A supplementary candidate is discarded if the angle sum makes it impossible.

Reasoning checklist · self / teacher assessment

Think first. Reveal a hint when the class is ready.

Teacher preparation and assessment

Connect geometric and algebraic forms of applications of plane vectors.
Geometry: Vectors yield metric relations, sine and cosine rules, and triangle centres.
Physical quantities: Add forces as vectors; calculate work with a dot product.
Close with: conditions → representation → reasoning → check.

Expected reasoning: Vectors yield metric relations, sine and cosine rules, and triangle centres.
Expected reasoning: Add forces as vectors; calculate work with a dot product.
Expected correction: An SSA triangle may have two valid configurations.