Law of Sines for Angles Problem: You can use the law of sines to find an unknown angle

Chapter 6, Problem 11

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Law of Sines for Angles Problem: You can use the law of sines to find an unknown angle measure, but the technique is risky. Suppose that ABC has sides 4 cm, 7 cm, and 10 cm, as shown in Figure 6-4f. Figure 6-4f a. Use the law of cosines to find the measure of angle A. b. Use the answer to part a (dont round) and the law of sines to find the measure of angle C. c. Find the measure of angle C again, using the law of cosines and the given side measures. d. Your answers to parts b and c probably do not agree. Show that you can get the correct answer from your work with the law of sines in part b by considering the general solution for arcsine. e. Why is it dangerous to use the law of sines to find an angle measure but not dangerous to use the law of cosines?

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