Exploring Ratios
In the last lesson, relationships were formulated between the three sides of special right triangles. In this exploration, the ratio of two sides of right triangles using slope ratios are compared.
Suppose that a school needs to build two ramps on their campus, and both ramps must have slope = \(\dfrac{1}{12}\) to be compliant with ADA guidelines.
Remember: Slope=\(\dfrac{\Delta y}{\Delta x} =\dfrac {rise}{run}=\dfrac {1}{12}\).
The first ramp must have a vertical change (rise) of 3 feet. The second ramp must have a vertical change (rise) of 5 feet.
- Calculate the horizontal run of each ramp given the vertical rise.
- Calculate the length of each ramp (hint: draw a right triangle to represent the base (ground), the hypotenuse (ramp) and height (vertical rise).
- What do you notice about the ratios of each ramp?
- What can you say about the two right triangles that form the ramps?
