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8-5 Law of Sines and Law of Cosines Objective Use the Law of Sines and the Law of Cosines to solve triangles. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines In this lesson, you will learn to solve any triangle. To do so, you will need to calculate trigonometric ratios for angle measures up to 180°. You can use a calculator to find these values. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Example 1: Finding Trigonometric Ratios for Obtuse Angles Use your calculator to find each trigonometric ratio. Round to the nearest hundredth. A. tan 103° Holt McDougal Geometry B. cos 165° C. sin 93° 8-5 Law of Sines and Law of Cosines Check It Out! Example 1 Use a calculator to find each trigonometric ratio. Round to the nearest hundredth. d. tan 175° Holt McDougal Geometry e. cos 92° f. sin 160° 8-5 Law of Sines and Law of Cosines You can use the Law of Sines to solve a triangle if you are given • two angle measures and any side length (____ or ____) or • two side lengths and a non-included angle measure (____). Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Example 2A: Using the Law of Sines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. FG Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Example 2B: Using the Law of Sines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mQ Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Check It Out! Example 2c Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. NP Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Check It Out! Example 2d Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mL Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Check It Out! Example 2e Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mX Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Check It Out! Example 2f Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. AC Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Check It Out! Example 2g Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines The Law of Sines cannot be used to solve every triangle. If you know two side lengths and the included angle measure or if you know all three side lengths, you cannot use the Law of Sines. Instead, you can apply the Law of Cosines. You can use the Law of Cosines to solve a triangle if you are given • two side lengths and the included angle measure (____) or • three side lengths (____). Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Helpful Hint The angle referenced in the Law of Cosines is across the equal sign from its corresponding side. Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Example 3A: Using the Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. XZ Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Example 3B: Using the Law of Cosines Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mT Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Check It Out! Example 3c Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. DE Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Check It Out! Example 3d Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mK Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Check It Out! Example 3e Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. YZ Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Check It Out! Example 3f Find the measure. Round lengths to the nearest tenth and angle measures to the nearest degree. mR Holt McDougal Geometry 8-5 Law of Sines and Law of Cosines Helpful Hint Do not round your answer until the final step of the computation. If a problem has multiple steps, store the calculated answers to each part in your calculator. Holt McDougal Geometry
