LEARN · EXPLAIN · REVISE

Find b using the sine rule.

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 / Standard#Worked example

a=2,\quad A=30^{\circ},\quad B=90^{\circ}

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

Match each side with its opposite angle.

Worked solution

Translate the geometry or physical quantity into vectors and check angle conventions.
Calculate or simplify this relation.
$b=a\frac{\sin B}{\sin A}=2\frac1{1/2}=4$
The side opposite the right angle is the longest.

The requested value is 4.

Checks and common pitfalls: The side opposite the right angle is the longest.

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.