There are several formulas for determining the size of an angle in a triangle from three known sides. The most convenient involves the versed sine of the angle, which means (1 -cos) of the angle. The formula goes as follows:

The value s means one-half the sum of sides a, b, and c, or

For the triangle shown in figure 1-30, you would determine the size of angle A as follows:

The angle with cosine 0.60333 measures (to the nearest minute) 5253.

Figure 1-30.Oblique triangle with three sides given and solved by versed sine formula.