In this class of problems, we are given a slope or ramp with some dimensions known, and we are asked to find the angle of the slope or ramp.

A ramp has been built to make a stage wheelchair accessible. The building inspector needs to find the angle of the ramp to see if it meets regulations. He has no instrument for measuring angles. With a tape measure, he sees the stage is 4t high and the distance along the ramp is 28ft.

Include all the information given and label the measure we are asked to find as *x*.
Draw it as close to scale as you can.

Right Triangle Toolbox

Reviewing what we are given and what we need:

- We are asked to find
*x*, the angle at which the ramp goes up to the stage. - We are given the hypotenuse (AB) and the side opposite the angle

Inserting the values given and the unknown x:
Using a calculator,
divide 4 by 28:
What angle has 0.1429 as its sine? For this we use the inverse function arcSine.
It tells us what angle has a given sine.

Using a calculator*
again, we find that arcSin(0.1429) is 8.22°, so

x = 8.22°

We see from our calculation that the ramp angle is somewhere around 9°. Looking at our diagram we see this looks about right.

If you get a very different answer,
**the most common error** is not setting the calculator to work in degrees or radians as needed.

Repeat this problem with a stage height of 8ft. The ramp angle should come out to about 16.6°.

- Angle definition, properties of angles
- Standard position on an angle
- Initial side of an angle
- Terminal side of an angle
- Quadrantal angles
- Coterminal angles
- Reference angle

- Introduction to the six trig functions
- Functions of large and negative angles
- Inverse trig functions
- SOH CAH TOA memory aid
- Sine function (sin) in right triangles
- Inverse sine function (arcsin)
- Graphing the sine function
- Sine waves
- Cosine function (cos) in right triangles
- Inverse cosine function (arccos)
- Graphing the cosine function
- Tangent function (tan) in right triangles
- Inverse tangent function (arctan)
- Graphing the tangent function
- Cotangent function cot (in right triangles)
- Secant function sec (in right triangles)
- Cosecant function csc (in right triangles)

- The general approach
- Finding slant distance along a slope or ramp
- Finding the angle of a slope or ramp

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