Choosing a Triangle Method
Decide from what a question gives you which tool a triangle needs: Pythagoras, right-angle ratios, the sine rule or the cosine rule.
What a learner can do afterwards
- Sort triangle questions by what is given before calculating anything
- Say why the chosen rule is the only one that fits the given information
- Spot a diagram that has to be split into two triangles solved in order
1 · Read
Sort the question before you solve it. A right-angled triangle with two known sides needs Pythagoras. A side paired with its opposite angle needs the sine rule. Two sides trapping their angle, or all three sides, need the cosine rule.
You know two angles and one side. Find the third angle from 180 degrees, and you now own a side with its opposite angle. That pair is the fingerprint of the sine rule, so use it.
You know two sides with the angle trapped between them. No side pairs with an opposite angle, so the sine rule cannot start. Only the cosine rule fits, and saying why earns method marks.
Some diagrams split into two right-angled triangles solved in order. In a 6, 8 and 10 triangle the missing leg is 8, and that side becomes a known side of the next triangle. Solve the first, carry the shared side across, then solve the second.
Name what is given, match it to one rule, and split shared-side diagrams into two ordered steps.
2 · Watch
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Where it sits
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.