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.

http://www.mathsisfun.com/algebra/trig-finding-angle-right-triangle.html
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.

adjacent-opposite-hypotenuse.gif
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:
SOH...
Sine: sin(θ) = Opposite / Hypotenuse
...CAH...
Cosine: cos(θ) = Adjacent / Hypotenuse
...TOA
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)?

http://www.wolframalpha.com
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.