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GEOMETRY MODULE 2 LESSON 33 APPLYING THE LAWS OF SINES AND COSINES OPENING EXERCISE Complete the Opening Exercise in your workbook. MOD2 L33 Law of Sines Law of Cosines Pythagorean Theorem Law of Sines or Law of Cosines Law of Sines 1 PRACTICE Example 1: Find the missing side length in ∆𝐴𝐵𝐶. Which method should we use to find length AB? Explain. The law of sines can be used because we are given information about two of the angles and one side. We can use the triangle sum theorem to find the measure of angle C. Why can’t we use the Pythagorean Theorem with this problem? We can only use the Pythagorean Theorem with right triangles. The given triangle is not a right triangle. Why can’t we use the law of cosines with this problem? The law of cosines requires that we know the lengths of two sides of the triangle. We are only given information about the length of one side. Write the equation to find the length of AB. sin 75 sin 23 = 2.93 𝐴𝐵 Find AB and round the length to the tenths place. sin 75 sin 23 = 2.93 𝐴𝐵 𝐴𝐵 sin 75 = 2.93 sin 23 𝐴𝐵 = 2.93 sin 23 = 1.18 sin 75 𝐴𝐵 = 1.2 MOD2 L33 2 Example 2: Find the missing side length in ∆𝐴𝐵𝐶. Which method should we use to find length AC? Explain. We do not have enough information to use the law of sines because we do not have enough information to write any of the ratios related to the law of sines. We can use law of cosines because we are given two side lengths and the included angle. Write the equation that to find the length of AC. 𝑥 2 = 5.812 + 5.952 − 2(5.81)(5.95) cos 16 Find AC and round the length to the tenths place. 𝑥 2 = 5.812 + 5.952 − 2(5.81)(5.95) cos 16 𝑥 = √5.812 + 5.952 − 2(5.81)(5.95) cos 16 𝑥 = 1.64 𝑥 = 1.6 SUMMARY Pythagorean Theorem: Use when solving a right triangle. At least one complementary angle measure and one side measure must be known. Law of Sines: Use to solve acute (and obtuse triangles). There are two cases in which law of sines should be used – (1) when two angles and one side are known and (2). *when two sides and an angle are known. *This is a special case involving inverse trig functions. Law of Cosines: Use to solve acute (and obtuse triangles). Law of cosines should be used when two sides and the included angle is known. GROUP ACTIVITY Complete Exercises 1, 2, and 3 in your workbook. Turn in by the end of class. MOD2 L33 3