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2. Solve the triangle given below α 5 B Y B C Based on the length of the sides, which of the unknown angles has the largest measure? What is the degree measure of this angle? • Which of the remaining unknown angles has a lesser measure based on their opposite sides? What is the degree measure of this angle? ● What is the degree measure of the remaining unknown angle? 7

2. Solve the triangle given below α 5 B Y B C Based on the length of the sides, which of the unknown angles has the largest measure? What is the degree measure of this angle? • Which of the remaining unknown angles has a lesser measure based on their opposite sides? What is the degree measure of this angle? ● What is the degree measure of the remaining unknown angle? 7

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter3: Triangles
Section3.5: Inequalities In A Triangles
Problem 39E
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Sample Problems (Time allotment: 20 minutes) Let us apply the Law of Cosines in solving the problem in Situation 1. Example 1 (SAS) Find the value of b in the figure below. B 12 A α b Y Solution. We are given a scenario wherein two sides and their included angle (SAS) are known. From these, we are to determine the side opposite the included angle. Using the Law of Cosines Eq. 2 b²=a²+c²-2ac cos B Substituting the given values, we have b² 10²+122-2(10)(12) cos 67° b² 100+144-240 cos 67° b=√100+144-240 cos 67° 12.3 Referring to the same problem, this time let us determine the remaining angle measures, namely, a and y. We can use either Law of Sines or Law of Cosines to find these values. Using the Law of Sines sin 67° sin a 10 12.3 10 sin 67° sin α = 12.3 a=sin 10sin 67° ≈48.5° 12.3 And for the last angle, we can apply the Triangle Sum Theorem. y=180° -67°-48.5° = 64.5° Mathematics 4 Page 3 of 6 67° 10
Transcribed Image Text:Sample Problems (Time allotment: 20 minutes) Let us apply the Law of Cosines in solving the problem in Situation 1. Example 1 (SAS) Find the value of b in the figure below. B 12 A α b Y Solution. We are given a scenario wherein two sides and their included angle (SAS) are known. From these, we are to determine the side opposite the included angle. Using the Law of Cosines Eq. 2 b²=a²+c²-2ac cos B Substituting the given values, we have b² 10²+122-2(10)(12) cos 67° b² 100+144-240 cos 67° b=√100+144-240 cos 67° 12.3 Referring to the same problem, this time let us determine the remaining angle measures, namely, a and y. We can use either Law of Sines or Law of Cosines to find these values. Using the Law of Sines sin 67° sin a 10 12.3 10 sin 67° sin α = 12.3 a=sin 10sin 67° ≈48.5° 12.3 And for the last angle, we can apply the Triangle Sum Theorem. y=180° -67°-48.5° = 64.5° Mathematics 4 Page 3 of 6 67° 10
2. Solve the triangle given below A 5 α В Y ● Based on the length of the sides, which of the unknown angles has the largest measure? What is the degree measure of this angle? • Which of the remaining unknown angles has a lesser measure based on their opposite sides? What is the degree measure of this angle? ● What is the degree measure of the remaining unknown angle? B 7
Transcribed Image Text:2. Solve the triangle given below A 5 α В Y ● Based on the length of the sides, which of the unknown angles has the largest measure? What is the degree measure of this angle? • Which of the remaining unknown angles has a lesser measure based on their opposite sides? What is the degree measure of this angle? ● What is the degree measure of the remaining unknown angle? B 7
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