PYTHAGOREAN THEOREM

Trigonometry PYTHAGOREAN THEOREM Rev. 0 Page 1 MA-04 Figure 1 Triangle PYTHAGOREAN THEOREM This chapter covers right triangles and solving for unknowns using the Pythagorean theorem. EO 1.1 Given a problem, APPLY the Pythagorean theorem to solve for the unknown values of a right triangle. Trigonometry is the branch of mathematics that is the study of angles and the relationship between angles and the lines that form them. Trigonometry is used in Classical Physics and Electrical Science to analyze many physical phenomena. Engineers and operators use this branch of mathematics to solve problems encountered in the classroom and on the job. The most important application of trigonometry is the solution of problems involving triangles, particularly right triangles. Trigonometry is one of the most useful branches of mathematics. It is used to indirectly measure distances which are difficult to measure directly. For example, the height of a flagpole or the distance across a river can be measured using trigonometry. As shown in Figure 1 below, a triangle is a plane figure formed using straight line segments (AB, BC, CA) to connect three points (A, B, C) that are not in a straight line. The sum of the measures of the three interior angles (a', b', c') is 180- , and the sum of the lengths of any two sides is always greater than or equal to the third. Pythagorean Theorem The Pythagorean theorem is a tool that can be used to solve for unknown values on right triangles. In order to use the Pythagorean theorem, a term must be defined. The term hypotenuse is used to describe the side of a right triangle opposite the right angle. Line segment C is the hypotenuse of the triangle in Figure 1. The Pythagorean theorem states that in any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides. This may be written as c = a + b or . (4-1) 2 2 2