Special Right Triangles: Printable Notes
In this
lesson2, you will investigate two special right triangles. These triangles are
In Module
9 Lesson
45o 45o 90o and 30o 60o 90o triangles. You can use trigonometric ratios and the
Pythagorean Theorem to find missing sides lengths in these triangles like you can with any right
triangle. But you will be dealing with these two special triangles many times in lots of math
classes and in tests such as SAT tests or college placement tests, so it¶VDJRRGLGHDWR
memorize the relationships among their sides.
Let¶VEHJLQZLWKWKH 45o 45o 90o triangle. A right triangle is isosceles if and only if it¶VD
45o 45o 90o triangle. The legs are congruent and the length of the hypotenuse is the square
root of 2. Most of the problems associated with this triangle involve knowing a side length or
knowing the hypotenuse length. When you know one side length, the other side length has to
be equal to it and the hypotenuse length is the side length multiplied by
the length of the hypotenuse, you divide it by
Example 1
2 . When you know
2 to find the length of each leg.
Example 2
Give these problems a try. You can find the answers at the end of these notes.
Next, let¶VH[SORUHWKH 30o 60o 90o triangle. All 30o 60o 90o triangles are scalene, so you
will always have three different side lengths. You will have a short side, a long side and a
hypotenuse. These sides are also related. The length of the hypotenuse is twice the length of
the short leg. The length of the long leg is the square root of three times the length of the short
leg. You always want to know the length of the short leg when dealing with 30o 60o 90o
triangles because it¶VHDV\WRGHWHUPLQHWKHRWKHUVLGHOHQJWKVLI\RX know it.
If you know the length of the hypotenuse, divide it by 2 to find the length of the short leg. If you
know the length of the long leg, divide it by
Example 3
3 to find the length of the short leg.
Example 4
Example 5
Here are some practice problems for 30o 60o 90o triangles. Find the missing side lengths
and give answers in simplest radical form.