Geometry and Solid Figures: Special Right Triangles

A special right triangle is a triangle whose sides are in a particular ratio.

Two special right triangles are and triangles.

In a special triangle, the three angles are , and .

The lengths of the sides of this triangle are in the ratio of
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In a special triangle , the three angles are

The lengths of this triangle are in the ratio of .

Examples:
Example 1.  Find the length of the hypotenuse of a right triangle if the length of the other two sides are both 4 inches.
Solution: this is a right triangle with two equal sides. Therefore, it must be a triangle. Two equivalent sides are inches. The ratio of sides:
The length of the hypotenuse is inches.

Example 2.  The length of the hypotenuse of a right triangle is 6 inches. What are the lengths of the other two sides if one angle of the triangle is ?
Solution: The hypotenuse is inches and the triangle is a triangle.  Then, one side of the triangle is (it’s half the side of the hypotenuse) and the other side is . (it’s the smallest side times )