Mon Prof Augmenté
Ramp with Right Triangles
Age 14 · Maths
A ramp and upright posts make several right-angled triangles that share the same acute corner. For that angle, the ratios of the sides stay fixed, and Pythagoras connects the three side lengths.
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In the picture
- The acute angle where the plank meets the ground
- The vertical post: the side opposite the acute angle
- The ground segment: the side next to the acute angle
- The sloping plank: the hypotenuse
Examples
- A wheelchair ramp with a steady slope
- A ladder leaning against a wall
Key takeaways
- For a fixed acute angle, the side ratios are the same in every similar right-angled triangle.
- Pythagoras relates all three sides, while trigonometric ratios relate an angle to two sides.
Quiz: Ramp with Right Triangles (Age 14)
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In right-angled triangles that share the same acute angle, what happens to the ratios of corresponding sides?
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In the ramp triangles, which side is opposite the acute angle where the plank meets the ground?
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According to the card, what does Pythagoras connect in a right-angled triangle?
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