In this class of problems, we are given an angle and some other measures, and asked to find the distance up a slope or ramp.

We are designing a ramp up to a stage to make it wheelchair accessible. The stage is 4 ft high, and building regulations state that the ramp angle must be 9°. How long will the ramp be, measured along its slope?

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.

Reviewing what we are given and what we need:

- We are asked to find
*x*, the hypotenuse of the right triangle ABC. - We are given an angle and the side opposite that angle

Right Triangle Toolbox

We see from our calculation that the ramp length is roughly 6 times the stage height. 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 length should come out to double the above.

Why? All 9° right triangles are similar (AAA), and in similar triangles all corresponding sides remain in the same ratio. So if you double one side (the side BC) the others will all double also.

- 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

(C) 2011 Copyright Math Open Reference.

All rights reserved

All rights reserved