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28
7 × 4 = 28.
Class 9 · English Version · Mathematics
Geometry, measurement and trigonometry readiness
Connect measurement, geometry and trigonometry with labelled diagrams.
About this lesson and its coverage
Shared cross-level core and stretch unit. Start with the core questions, then use the stretch example for deeper work. The same unit is available in related class and board pathways; it is not a full grade-specific or examination-specification course. A teacher should select the appropriate depth and further topics.
Learn the idea
A diagram must show which lengths and angles are known. Area uses square units and volume cubic units. Pythagoras applies to right-angled triangles: a² + b² = c², with c opposite the right angle. Trigonometric ratios also refer to a selected angle.
Worked example
A right triangle with legs 6 cm and 8 cm has hypotenuse √(36 + 64) = 10 cm. For the angle opposite the 6 cm leg, sin θ = 6/10 = 0.6.
- Draw and label before calculating.
- Choose the relationship that matches the diagram.
- Check units and whether the size is sensible.
Stretch example
For vectors a = (1,2) and b = (3,−1), a·b = 1. Their magnitudes are √5 and √10, so cos θ = 1/√50. A scalar product connects coordinate geometry to the angle between vectors.
Your written practice
Show your working on paper. Check your answer, then choose Next.
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70
180 − 50 − 60 = 70.
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13
√(25 + 144) = 13.
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24
2 × 3 × 4 = 24.
Write in your own words. A guardian or teacher should review this response.
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The right angle must be given or established, not assumed from appearance.
Separate stated conditions from a diagram’s appearance.
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10
2 × 3 + 1 × 4 = 10.
Write in your own words. A guardian or teacher should review this response.
Show model answer and explanation
Distance = |−10|/√(3²+4²) = 2 units.
Use the point-to-line formula with the absolute value and correct denominator.
Progress and browser storage
Notebook challenge, sources and further study
Design on paper
Draw a scale plan for a rectangular study area with one triangular section.
Review with a guardian or teacher
- State the scale and real dimensions.
- Calculate area with consistent units.
- Explain which measurements would need checking on site.
Keep your work on paper or in a local file. This page does not upload it or automatically grade the project.
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