Angle+of+Incline

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.

**T**an (x) = **O**pposite / **A**djacent = 4.5 / 18 = **0.25**
 * **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**. ||  || [[image:adjacent-opposite-hypotenuse.gif]] ||
 * Step 2**: now use the first letters of those two sides (**O**pposite and **H**ypotenuse) and the phrase "[|SOHCAHTOA]" to find which one of Sine, Cosine **or** Tangent to use:
 * **//SOH...//** || **S**ine: sin(θ) = **O**pposite / **H**ypotenuse ||
 * **//...CAH...//** || **C**osine: cos(θ) = **A**djacent / **H**ypotenuse ||
 * **//...TOA//** || **T**angent: tan(θ) = **O**pposite / **A**djacent ||
 * Step 3**: Put our values into the Sine 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°**
 * Step 4**: Now solve that equation!
 * 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.