Given the figure below, find the length of .
Step 1: Establish that and are similar.
and are vertical angles, so they are equal in measure.
Two right-angled triangles are similar to each other if an acute angle in
one triangle is equal to the measure of an acute angle in the
other. Therefore, is similar to .
Step 2: Find the length of .
Since is similar to , their side lengths are proportional.
Using Pythagoras' theorem, write a proportion to show the length of . Solve for the length of .