5.1 Right Triangle Trigonometry

Introduction The word trigonometry (from the Greek trigonon meaning “triangle” and metria meaning “measurement”) refers to the measurement of triangles. In Section 4.2 we defined the trigonometric functions using coordinates of points on the unit circle and by using radian measure we were able to define the trigonometric functions of any angle. In this section we will show that the trigonometric functions of an acute angle in a right triangle have an equivalent definition in terms of the lengths of the sides of the triangle.

Terminology In FIGURE 5.1.1(a)1 we have drawn a right triangle with sides labeled a, b, and c (indicating their respective lengths) and one of the acute angles denoted by ?. From the Pythagorean theorem we know that