MAT 110 Chapter 9 Study Guide
MAT 110 Chapter 9 Study Guide MAT 110
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This 5 page Study Guide was uploaded by Sterling on Wednesday September 14, 2016. The Study Guide belongs to MAT 110 at Barry University taught by Dr. Singh in Fall 2016. Since its upload, it has received 6 views. For similar materials see Precalculus Mathematics 2 in Mathmatics at Barry University.
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Date Created: 09/14/16
MAT 110 Precalculus Mathematics 2 Chapter 9 Study Guide Notes L. Sterling September 22nd, 2016 Abstract Provide a generalization to each of the key terms listed in this section. 1 True and Untrue about Right Triangles ▯ Untrue: You can solve a right triangle if you know what the two acute angles are. ▯ True: You can solve a right triangle if you know what the two sides are. 2 Cases 2.1 SSS Side ▯ Side ▯ Side 1 2.2 SAS Side ▯ Angle ▯ Side 2.3 SSA Side ▯ Side ▯ Angle 2.4 sSA Short Side ▯ Long Side ▯ Angle 2.5 SsA Long Side ▯ Short Side ▯ Angle 2.6 AAS Angle ▯ Angle ▯ Side 2.7 ASA Angle ▯ Side ▯ Angle 2.8 AAA Angle ▯ Angle ▯ Angle 3 Law of Sines Sides : a; b; c Opposite angles : A; B; C 2 3.1 Theorem sin A sin B sin C = = a b c 4 Second Part of Theorem sin A sin B = a b sin A sin C a = c sin B sin C = b c A + B + C = 180▯ 5 Law of Cosines Sides : a; b; c Opposite angles : A; B; C 5.1 Theorem c = a + b ▯ 2ab cos C b = a + c ▯ 2ac cos B 2 2 2 a = b + c ▯ 2bc cos A 3 6 Area of a Triangle 6.1 Formula 1 K = bh 2 6.2 Parts of the Formula K : Area b : Base h : Altitude 7 Finding the area of any SAS Triangles 7.1 Formulas 1 K = ab sin C 2 1 K = bc sin B 2 1 K = ac sin A 2 7.2 De▯nition The triangles area is a half of the product of two of the given sides times the included angles sine. 8 Herons Formula 8.1 Formula K = p s(s ▯ a)(s ▯ b)(s ▯ c) 4 8.2 Parts of the Formula K : Area Sides : a; b; c s = 1(a + b + c) =a + b + c 2 2 5
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