Technical Mathematics, Sixth Edition

Chapter 6. Geometry

OBJECTIVES When you have completed this chapter, you should be able to Find the angles formed by intersecting straight lines. Solve practical problems that require finding the sides and angles of right triangles. Solve practical problems in which the area of a triangle or a quadrilateral must be found. Solve applications problems involving the circumference, diameter, and area of a circle, or the tangent to a circle. Compute surface areas and volumes of spheres, cylinders, cones, and other solid figures.

Geometry is a very old branch of mathematics. The word geometry, or geo-metry, means earth measure and probably refers to the ancient Egyptians' use of knotted ropes to measure the land so that boundary markers could be replaced after the annual flooding of the Nile. Geometry was developed by Pythagoras, Euclid, Archimedes, and many others and was included in the quadrivium, the four subjects needed for a bachelor's degree in the Middle Ages. We can only hint at that rich history here, confining ourselves mostly to the practical and very important computation of dimensions, areas, and volumes of the plane and solid geometric figures that we encounter in technical work. For example, how would you compute the volume, and hence the weight, of the bored hexagonal stock of Fig. 6-1? Here we will show how.

Further, our introduction to angles and triangles will prepare us for our later study of trigonometry. We will touch only on Euclidean geometry in this chapter and ...