Side Length Ratios Exploration

Ben Graber
One of the most useful properties of similar shapes is that the ratio of side lengths are always equal to each other regardless of the size of the shapes. This fact was used to estimate the distance from the earth to the sun thousands of years ago and is used even more frequently today to make calculations in engineering, architecture, and thousands of other applications. When a person wants to use the properties of similar right triangles to create a ratio, he or she will consider one of the non-right angles to be the reference angle. In the applet below we'll call the angle at point A the reference angle. The hypotenuse is the long side of the triangle, the side that is opposite the right angle. The leg that is next to the reference angle (AB below) is called the "adjacent" side. The leg that does not touch the reference angle (BC below) is called the "opposite" side.