4.3. Special Right Triangles http://www.ck12.org
TABLE4.3:(continued)
x x√ 3 2 x
1818 =x√ 3
√^18
3 =x
x= √^183 = √^183 ·√ 3
√ 3 =^18
√ 3
3 =^6
√ 3
Note that you need to rationalize denominators.
Concept Problem Revisited
If you can recognize the pattern for 45-45-90 right triangles, a right triangle with legs 6 inches and 6 inches has a
hypotenuse that is 6√2 inches.x= 6 √2.
Vocabulary
Corresponding angles and sidesare angles and sides that are on opposite sides of each other in a triangle. Capital
letters likeA,B,Care often used for the angles in a triangle and the lower case lettersa,b,care used for their
corresponding sides (angleAcorresponds to side a etc).
Pythagorean number triplesare special right triangles with integer sides.
A45-45-90 triangleis a special right triangle with angles of 45◦, 45 ◦, and 90◦.
A30-60-90 triangleis a special right triangle with angles of 30◦, 60 ◦, and 90◦.
Guided Practice
Using your knowledge of special right triangle ratios, solve for the missing sides of the following right triangles.