Geometry and TrigonometryVery hardRise of a ramp from its tangent and length
Geometry and Trigonometry practice question
A straight ramp rises at an angle whose tangent is 3/4. The sloped surface of the ramp is 20 metres long. How many metres higher is the top of the ramp than the bottom?
Answer: 12
A tangent of 3/4 means rise : run = 3 : 4, a 3-4-5 shape, so the sloped length is 5 parts. Each part is 20/5 = 4 metres, and the rise is 3 parts: 12 metres. (Equivalently, sin = 3/5 and 20 × 3/5 = 12.)
Common wrong answers
- If you answered 15
- 15 is 20 × 3/4, applying the tangent to the sloped length; the tangent relates rise to run, not to the slope.
- If you answered 16
- 16 is the horizontal RUN (4 parts × 4 metres), not the rise.
- If you answered 26.67
- 26.67 is 20 × 4/3, inverting the ratio — and a rise can't exceed the ramp's length.
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