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4
c²=16+16−32×0.5=16.
Class 10 · English Medium · Cambridge · Mathematics
Geometry, measurement and trigonometry readiness
Use non-right-triangle rules and circle geometry with known conditions.
About this lesson and its coverage
Original Kidemy Class 10 progression. This level has its own text, examples and questions. Curriculum versions share the progression; complete board-specific coverage still needs specification matching and additional material.
Learn the idea
For a triangle, the cosine rule c²=a²+b²−2ab cosC uses the included angle. The sine rule relates sides to opposite angles, but an ambiguous case can produce two triangles. Label correspondence before substituting.
Worked example
With a=b=5 and included angle60°, c²=25+25−50×0.5=25, so c=5.
- Identify the quantities and restrictions.
- Show a method with units or symbols.
- Check and explain the result.
Your written practice
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50
The circumference angle is half under the same-arc condition.
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90
The radius is perpendicular to the tangent.
Write in your own words. A guardian or teacher should review this response.
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The subtraction term uses the angle between the two known sides.
Match labels to the correct angle.
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Sine has the same positive value for θ and 180°−θ; both may fit the remaining conditions.
Check feasibility rather than accepting both automatically.
Progress and browser storage
Notebook challenge, sources and further study
Apply the idea
Draw two triangles from given measurements and discuss whether they are uniquely determined.
Review with a guardian or teacher
- Use the stated evidence or givens.
- Show reasoning rather than only a result.
- Review and explain one correction.
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