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Boss lesson · The Ramp Inspection
Exam-hall rules, one ramp
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Exam-hall rules, one ramp

This is the boss. No calculator — the numbers are 3-4-5 clean and the inspector’s card carries the one tangent fact you’ll need. One loading-dock ramp, and every answer feeds the next: the slope length by Pythagoras, then the grade from rise over level run, then the angle off the card, then the verdict against the code. Write each line down — one early slip rolls downhill, and rolling downhill is the one thing ramps do best.

Everything from the chapter rides on this one. 5★ under par here takes the chapter crown. Clipboard out.

abc

a2+b2=c2a^{2} + b^{2} = c^{2}

  • aa= Leg a
  • bb= Leg b
  • cc= Hypotenuse c

each variable a length

Pythagorean Theorem solver →
θoa

tan⁡θ=oa\tan\theta = \frac{o}{a}

  • θ\theta= Acute angle (angle)
  • oo= Opposite side (length)
  • aa= Adjacent side (length)
Right-Triangle Tangent Ratio (TOA) solver →
GLΔh

G=100 ΔhLG = \frac{100\,\Delta h}{L}

  • GG= Grade (concentration)
  • Δh\Delta h= Vertical rise (length)
  • LL= Horizontal run (length)
Percent Grade from Rise and Run solver →
no calculator in the boss room — the numbers are chosen to fit in your head