LEARN · EXPLAIN · REVISE

Find the third side using the cosine 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#Your turn

a=4,\quad b=4,\quad C=60^{\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

The given angle is the included angle between a and b.

Worked solution

Translate the geometry or physical quantity into vectors and check angle conventions.
Calculate or simplify this relation.
$c^2=16+16-2(16)\cos60^{\circ}=16$
Take the positive square root for a side length.

The requested value is 4.

Checks and common pitfalls: Take the positive square root for a side length.

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.