Therefore, AC = 5, and tan ABC = , which is (B).
Special Right Triangles
Both of the previous questions you worked also used special right triangles. While in the last question we
used the Pythagorean Theorem to find the missing side, if you memorize these special triangles you can
avoid using the Pythagorean Theorem in a lot of cases.
Your Friend
the Rectangle
Be on the lookout for
problems in which the
application of the
Pythagorean Theorem is
not obvious. For example,
every rectangle contains
two right triangles.
That means that if you
know the length and
width of the rectangle,
you also know the length
of the diagonal, which
is the hypotenuse of
both triangles.ETS writes very predictable geometry questions involving right triangles, reusing certain relationships. In
these questions the triangles being used have particular ratios. There are two different types of special
right triangles. The first involves the ratio of sides and the second involves the ratio of angles.
The most common special right triangles with side ratios are known as Pythagorean triplets. Here are
ETS’s favorites:
If you memorize these two sets of Pythagorean triplets (3-4-5 and 5-12-13), you’ll often be able to find
the answer without using the Pythagorean Theorem. If you’re given a triangle with a side of 3 and a
hypotenuse of 5, you know right away that the other side has to be 4. Likewise, if you see a right triangle
with sides of 5 and 12, you know the hypotenuse must be 13.
Relax; It’s Just a Ratio