SECTION 8.2 The Law of Sines 559 ‘Are You Prepared?’ Answers 1. 4 2. 26.6° 3. 30° 86. Determine whether x 3 − is a factor of x x x x 2 21 19 3. 4 3 2 + − + − 87. Find the exact value of sin 12 . π 88. If f x x, ( ) = find f x f x 4 4 , ( ) ( ) − − for x 5, 4.5, and 4.1. = Round results to three decimal places. 89. Solve θ θ θ π − + = ≤ < 2sin sin 5 6 for 0 2 . 2 90. If the two triangles shown are similar, find x. x 14 3 8 91. If a 4th degree polynomial function with real coefficients has zeros of 2, 7, and 3 5, − what is the remaining zero? 92. Simplify e e e 1 2 1 . x x x 2 2 2 2 2 ( ) ( ) ( ) − + + 93. What is the remainder when P x x x x 2 3 7 4 3 ( ) = − − + is divided by x 2? + 94. Write the equation of a circle with radius r 5 = and center 4, 0 ( ) − in standard from. 95. Find the domain of ( ) = − − g x x 3 1 5. 2 Retain Your Knowledge Problems 86–95 are based on previously learned material. The purpose of these problems is to keep the material fresh in your mind so that you are better prepared for subsequent sections, a final exam, or later courses such as calculus. 8.2 The Law of Sines Now Work the ‘Are You Prepared?’ problems on page 566. • Trigonometric Equations (Section 7.3, pp. 493–498) • Difference Formula for the Sine Function (Section 7.5, p. 514) • Geometry Essentials (Section A.2, pp. A14–A19) • Approximating the Value of a Trigonometric Function (Section 6.2, pp. 405–406) • Approximating the Value of an Inverse Trigonometric Function (Section 7.2, pp. 488–489) PREPARING FOR THIS SECTION Before getting started, review the following: OBJECTIVES 1 Solve SAA or ASA Triangles (p. 560) 2 Solve SSA Triangles (p. 561) 3 Solve Applied Problems (p. 563) If none of the angles of a triangle is a right angle, the triangle is called oblique . An oblique triangle will have either three acute angles or two acute angles and one obtuse angle (an angle measuring between ° 90 and ° 180 ). See Figure 18. In the discussion that follows, an oblique triangle is always labeled so that side a is opposite angle A, side b is opposite angle B, and side c is opposite angle C, as shown in Figure 19. Figure 18 (a) All angles are acute Obtuse angle (b) Two acute angles and one obtuse angle Figure 19 Oblique triangle c a b B C A
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