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?)"

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.

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 thenamesof the two sides you knowAdjacentis adjacent to the angle,Oppositeis opposite the angle,Hypotenuse.Step 2: now use the first letters of those two sides (Opposite andHypotenuse) and the phrase "SOHCAHTOA" to find which one of Sine, CosineorTangent to use:SOH...Sine: sin(θ) =Opposite /Hypotenuse...CAH...Cosine: cos(θ) =Adjacent /Hypotenuse...TOATangent: tan(θ) =Opposite /AdjacentStep 3: Put our values into the Sine equation:Tan (x) =Opposite /Adjacent = 4.5 / 18 =0.25Step 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.