Technical Mathematics, Sixth Edition

Chapter 7. Right Triangles and Vectors

OBJECTIVES When you have completed this chapter, you should be able to Find the trigonometric functions of an angle. Find the acute angle that has a given trigonometric function. Find the missing sides and angles of a right triangle. Solve practical problems involving the right triangle. Resolve a vector into components and, conversely, combine components into a resultant vector. Solve practical problems using vectors.

We have placed trigonometry early in the text because many technical students need this material for their physics course. If your students do not need this now, you may prefer to treat all the trigonometry topics in a single block later.

With this chapter we begin our study of trigonometry, the branch of mathematics that enables us to solve triangles. The trigonometric functions are introduced here and are used to solve right triangles. Other kinds of triangles (oblique triangles) are discussed in Chapter 8 and more applications of trigonometry are given later.

We also build on what we learned about angles and triangles in Chapter 6, mainly the Pythagorean theorem and the fact that the sum of the angles of a triangle is 180°. Briefly introduced in this chapter are vectors, the study of which will be continued in Chapter 8.

Triangles are everywhere: those we can see, like the triangles in a steel truss or formed by the support cables for an antenna, and those we cannot see, like the triangles a surveyor uses for triangulation, ...