g10-09-01 · Syllabus supplement
A triangle and three equal ratios
If one side changes scale, what happens to a/sinA?
1 MIN · PREDICT ON PAPER
Fix A=30°,B=60° and double side a. Predict all other sides and the three ratios.
Discuss or write first. No typed answer is required to continue.
The three ratios are equal; the opposite labels matter.
2 MIN · EXPLAIN AND REVISE
Which condition does your claim need?
Compare at least two cases. Write a reason, then check the explanation together.
Reveal explanation and conditions
The sine rule gives a/sinA=b/sinB=c/sinC=2R. Holding angles fixes shape; changing one side scales every side and the common ratio.
Conditions: Angles A,B,C are positive and sum to180°; opposite side labels must match.
Mathematical justification: Using altitudes, the area equals ab sinC/2=bc sinA/2=ca sinB/2; dividing gives the equal ratios.
1 MIN · EXIT CHECK
A=30°,B=90°,a=3. Find b.
Check after answering
b=3sin90°/sin30°=6.
Teacher guidance and extension
Before: Triangle angles, sine and cosine.
Ask: Which angle lies opposite the side labelled a?
Watch for: Pairing a side with an adjacent angle.
Challenge: Explain why the common ratio changes under enlargement even though the angles do not.
Suggested timing: predict 1 min, compare 3 min, explain 2 min, exit check 1 min. Observations can suggest a claim; they do not prove it for every input.
Optional local notebook
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