Problem Solving with the Sine Rule, Cosine Rule, and Area

Eight exam-style questions that mix the sine rule, the cosine rule, and the area formula — because the real skill in this lesson is choosing the right tool, not just running it. Whenever you are stuck, you have four kinds of help, in this order:

🤔 Socratic prompt — a question to get you thinking. 💡 Hint — a piece of method. ✅ Check my answer — try as many times as you like. 👀 Worked solution — the full method, unlocked once you have genuinely tried.

Give angles in degrees to 1 decimal place and lengths to 2 decimal places unless told otherwise. Keep full accuracy in your working and round only at the end. Calculator must be in degrees mode.

💛 Reflection

Before you close this, take a moment:

On each question, what was the first thing you looked for to decide which rule to use? If you can name that habit, you can repeat it under pressure.
Which felt harder — knowing which tool to reach for, or carrying out the calculation once you had chosen? Whichever it was tells you what to practise next.
Where a problem needed two tools in sequence, did you spot the intermediate quantity (a side or an angle) that unlocked the next step? That look-ahead is the heart of synthesis.
Did any answer come out feeling the wrong size? Sense-checking against the picture — biggest side opposite biggest angle — is a real skill, not a luxury.

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Problem Solving with the Sine Rule, Cosine Rule & AreaPure 1, Trigonometry · Lesson 3 (synthesis)

💛 Reflection

Problem Solving with the Sine Rule, Cosine Rule & Area
Pure 1, Trigonometry · Lesson 3 (synthesis)