One Angle and Two Sides

The third type of triangle illustrated is one in which one angle and the length of the two adjacent sides is known, Figure 13.11.

The limitations on this method are that the angle must be less than 90° and the at least one angle must be known or measured. The equation for area (A) is:

where A = Area; b = Known side; c = Known side; 0 = Angle between sides b and c; sine = Sine trigonometric function.

This equation is very useful in situations where one side of the triangle cannot be measured.

Rectangle, Square, and Parallelogram 185 C

Rectangle, Square, and Parallelogram 185 C

FIGURE 13.11. Triangle with one angle and the adjacent sides known.

Problem: Determine the area (ft2) of a triangle with sides of 350.0 ft and 555.0 ft and an included angle of 45°.

Solution:

A=-xaxbx sine 0 = - x 350.0 ft x 555.0 ft x sine 45 2 2

137355.4922

0 0

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