Ramp and Incline Design

  • 10th Grade
Reviewed by Cierra Henderson
Cierra Henderson, MBA |
K-12 Expert
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 13 | Questions: 20 | Updated: Jan 21, 2026
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1) A wheelchair ramp must rise 0.75 m over a horizontal distance of 9 m. What is the angle of inclination?

Explanation

θ = arctan(0.75/9) ≈ 4.76° → 5°.

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About This Quiz
Ramp and Incline Design - Quiz

Ramps aren’t just about accessibility — they’re precision-engineered structures based on slope and angle. In this quiz, you’ll calculate incline angles, rises, and lengths using trigonometry. From gentle wheelchair ramps to steep construction inclines, you’ll learn how math ensures safety, comfort, and compliance with design standards. By the end, you’ll... see moreunderstand how simple ratios create smooth and functional slopes everywhere around us.
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2)
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2) A ramp makes a 12° angle with the ground and is 5 m long. What vertical height does it rise to (nearest tenth)?

Explanation

Rise = 5·sin12° ≈ 1.04 m → 1.0 m.

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3) An accessibility ramp must rise 0.9 m over a horizontal run of 7 m. Find its angle.

Explanation

θ = arctan(0.9/7) ≈ 7.33° → 7°.

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4) A ramp has an incline of 10°. If the horizontal run is 12 m, what is the rise (nearest tenth)?

Explanation

Rise = 12·tan10° ≈ 2.12 m → 2.1 m.

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5) A 6 m long ramp rises 1.5 m. Find its angle (nearest degree).

Explanation

θ = arcsin(1.5/6) ≈ 14.48° → 14°.

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6) A 10 m long ramp makes an angle of 20°. How high does it rise?

Explanation

Rise = 10·sin20° ≈ 3.42 m → 3.4 m.

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7) A ramp must rise 1.5 m at a 12° angle. Find the ramp’s length.

Explanation

Length = 1.5 / sin12° ≈ 7.21 m → 7.2 m.

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8) A ramp rises 2 m over a horizontal run of 20 m. Find its angle.

Explanation

θ = arctan(2/20) ≈ 5.71° → 6°.

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9) A 15 m ramp makes an angle of 18°. Find the rise.

Explanation

Rise = 15·sin18° ≈ 4.64 m → 4.6 m.

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10) A ramp must rise 0.6 m at a 7° angle. Find its horizontal run.

Explanation

Run = 0.6 / tan7° ≈ 4.89 m → 4.9 m.

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11) A 20 m ramp makes an angle of 25°. Find its vertical rise.

Explanation

Rise = 20·sin25° ≈ 8.45 m → 8.5 m.

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12) A 12 m long ramp makes an angle of 15°. Find the rise.

Explanation

Rise = 12·sin15° ≈ 3.11 m → 3.1 m.

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13) A ramp must rise 1.5 m with a 6° angle. Find its length.

Explanation

Length = 1.5 / sin6° ≈ 14.36 m → 14.4 m.

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14) A ramp must rise 3 m over a 20 m horizontal distance. Find its angle.

Explanation

θ = arctan(3/20) ≈ 8.53° → 9°.

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15) A ramp rises 1.2 m over a horizontal distance of 10 m. Find its angle of inclination.

Explanation

θ = arctan(1.2/10) ≈ 6.84° → 7°.

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16) A 4 m long ramp rises 1 m vertically. Find its angle of inclination.

Explanation

θ = arcsin(1/4) ≈ 14.48° → 14°.

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17) A ramp rises 0.5 m and makes an angle of 5°. Find the horizontal run (nearest tenth).

Explanation

Run = 0.5 / tan5° ≈ 5.72 m → 5.7 m.

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18) A ramp has a 9° angle and a 6 m horizontal run. Find its vertical rise.

Explanation

Rise = 6·tan9° ≈ 0.95 m → closer to 1.0 m.

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19) A ramp must rise 2.4 m with a 10° angle. Find its horizontal run.

Explanation

Run = 2.4 / tan10° ≈ 13.61 m → 13.6 m.

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20) A 25 m long ramp makes an angle of 30°. Find the rise.

Explanation

Rise = 25·sin30° = 12.5 m.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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A wheelchair ramp must rise 0.75 m over a horizontal distance of 9 m....
A ramp makes a 12° angle with the ground and is 5 m long. What...
An accessibility ramp must rise 0.9 m over a horizontal run of 7 m....
A ramp has an incline of 10°. If the horizontal run is 12 m, what is...
A 6 m long ramp rises 1.5 m. Find its angle (nearest degree).
A 10 m long ramp makes an angle of 20°. How high does it rise?
A ramp must rise 1.5 m at a 12° angle. Find the ramp’s length.
A ramp rises 2 m over a horizontal run of 20 m. Find its angle.
A 15 m ramp makes an angle of 18°. Find the rise.
A ramp must rise 0.6 m at a 7° angle. Find its horizontal run.
A 20 m ramp makes an angle of 25°. Find its vertical rise.
A 12 m long ramp makes an angle of 15°. Find the rise.
A ramp must rise 1.5 m with a 6° angle. Find its length.
A ramp must rise 3 m over a 20 m horizontal distance. Find its angle.
A ramp rises 1.2 m over a horizontal distance of 10 m. Find its angle...
A 4 m long ramp rises 1 m vertically. Find its angle of inclination.
A ramp rises 0.5 m and makes an angle of 5°. Find the horizontal run...
A ramp has a 9° angle and a 6 m horizontal run. Find its vertical...
A ramp must rise 2.4 m with a 10° angle. Find its horizontal run.
A 25 m long ramp makes an angle of 30°. Find the rise.
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