Recall the ramps we discussed in the previous lesson. The ratio of the vertical rise to the horizontal run was \(1: 12\). What is the ratio defined as in terms of the sides in the triangle?

Refer back to the ramps again. Redraw and calculate the side lengths of the ramps (horizontal run and length of the ramp) using the 1:12 ratio. Find the measures of the angles formed by the rise, run and length of the ramp.

1) One ramp needs to have a vertical rise of 3 feet.

2) The other ramp needs to have a vertical rise of 5 feet.

Once calculations have been made, discuss the ratio of the vertical rise (opposite side) to the length of the ramp (hypotenuse), using the angle made by the ground and the ramp as the angle of reference.

Repeat this process for the ratio of the horizontal run of the ramp (adjacent side) to the hypotenuse. You should again see that the ratio is the same.

The ratio of the rise to the hypotenuse is called the sine and the ratio of the run to the hypotenuse is called the cosine.

This video will summarize this discovery:

## Go to Practice (Ratios for Special Right Triangles)