The altitude of the triangle ABC, segment DA, has been drawn. Derive a formula for the area of triangle BCA that depends on the measure of angle B along with side lengths a and c.

Triangle A B C is shown. A perpendicular bisector is drawn from point A to point D on side B C forming a right angle. The length of C B is a, the length of C A is b, the length of A B is c, and the length of A D is h.

Area = One-half(base)(height)

Following this setup:

Area = One-halfah

sin(B) = , so

h = , and

Area =