Problem: How steep of an angle can a robot climb without its wheels or tracks slipping?

To solve this, two students sent a robot up an ramp and kept increasing the incline.

They measured the length of the ramp and the height of the ramp.
From the site above it was determined that the angle of the ramp equaled the arc sin of the ramp's height over the ramp's length.

Step 1: find the names of the two sides you know
  • Adjacent is adjacent to the angle,
  • Opposite is opposite the angle,
  • and the longest side is the Hypotenuse.

Step 2: now use the first letters of those two sides (Opposite and Hypotenuse) and the phrase "SOHCAHTOA" to find which one of Sine, Cosine or Tangent to use:
Sine: sin(θ) = Opposite / Hypotenuse
Cosine: cos(θ) = Adjacent / Hypotenuse
Tangent: tan(θ) = Opposite / Adjacent
Step 3: Put our values into the Sine equation:
Tan (x) = Opposite / Adjacent = 4.5 / 18 = 0.25

Step 4: Now solve that equation!
Tan (x) = 0.25
Next, we can re-arrange that into this:
x = Tan-1 (0.25)
And then get our calculator, key in 0.5 and use the sin-1 button to get the answer:
x = 14°
Summary/Short Cut:

Our question became, "What is the arc tan of (the height divided by the length?)"

What is the arc tan of (4.5/18)?
We put our question into the site above and got our answer.

We also could have used a scientific calculator.
Using the computers calculator:
a) divide the height by the length
b) check the inverse/arc box
c) press the TAN key

We also could have looked up the result of dividing the height by the length in a table of trigonometric ratios.