of the formulas which can be derived from the relationship of their sides

and angles. These relationships enable one to make certain substitutions in

the general right triangle rule formula, and to derive certain constants

which hold true no matter what the size the right triangle is, just as long

as its angles are 45,, - 45,, or 30,, - 60,,.

b.

Derivation of the 45,, - 45,, Isosceles Triangle Relationship.

(1) In a 45,, - 45,, right triangle, as in any isosceles triangle, the sides

opposite the equal angles are equal.

Thus, in figure 23, side A can be

substituted for side B.

For example, if side A equals 2 inches, side B

would also equal 2 inches; therefore, the length of the hypotenuse, side C,

could be determined by multiplying the square root of one side by a value of

2.

In the following example we will show how the length of side C, the

hypotenuse, is derived by using side A as described above.

The last two

steps in this procedure serve to demonstrate that once the length of side C

has been found, the length of the two opposite sides can be determined by

multiplying the length of the hypotenuse or side C by the sine of either of

the 45,, angles. The following example demonstrates this process.

FIGURE 23.

FUNCTIONS OF A 45,, ANGLE.