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Unformatted text preview: Math 148 Lab 4 Trigonometry Spring Quarter, 2009 Due: Wednesday, June 3, 2009 Directions: Work out each problem, and use the work to fill out the answer sheet. Submit the answer sheet to your recitation instructor on or before the due date. Material from this lab will appear on the final exam. Late labs will not be accepted for grading. When you are asked to solve a triangle, you must find the lengths of all three sides and the measures of all three angles of the triangle. In a triangle problem, you will need to decide which methods to employ to solve the triangle based on the conditions that are given. Purpose: In sections 9.1 and 9.2, you used right triangle trigonometry (the Pythagorean Theorem and the definitions of sine, cosine, and tangent) to solve right trian- gles. In section 9.3 you used the Law of Cosines and in section 9.4 you will use the Law of Sines to solve oblique triangles (triangles that are not right triangles). The Law of Cosines c 2 = a 2 + b 2- 2ab cos C The Law of Sines a sin A = b sin B = c sin C 1 Part I: Getting Ahead When the Law of Cosines does not help you solve an oblique triangle, what do you do? No, you dont give up! Instead, seek another method. The next fact we use to solve oblique triangles is called the Law of Sines. The Law of Sines In triangle ABC, with the standard labeling of sides and angles as in the figure below, a sin A = b sin B = c sin C . C A B c b a Notice that the Law of Sines gives the equality of three ratios. Each ratio is the length of a side to the sine of the angle opposite that side. When working with the Law of Sines, we only use two of the three ratios at a time. The equation a sin A = b sin B has four unknowns: two sides and two angles. The Law of Sines is useful when three of these quantities are given. It then follows that the Law of Sines can be used to solve triangles that meet either of the following conditions: 1. Two sides and the angle opposite one of the sides are given (SSA). 2. Two angles and a side are given (AAS). Read through the following examples, and then work out the exercises that follow each example. We have only touched upon the Law of Sines. (You will learn more about the Law of Sines in lecture.) Inverse Sines Let be an angle in an oblique triangle. Then its sine will be a positive number which is less than...
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