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1. Solve the triangle given below C b Y 6 B 4 A • b = . Based on the length of the sides opposite them, which of the two unknown angles has a lesser measure? What is the degree measure of this angle? What is the degree measure of the remaining angle? 122° α

1. Solve the triangle given below C b Y 6 B 4 A • b = . Based on the length of the sides opposite them, which of the two unknown angles has a lesser measure? What is the degree measure of this angle? What is the degree measure of the remaining angle? 122° α

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter73: Achievement Review—section Seven
Section: Chapter Questions
Problem 30AR
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All values must be rounded off to 2 decimal places AND use these rounded off values when computing for other missing values. 1. Solve the triangle given below C 6 b B 4 A . b = • Based on the length of the sides opposite them, which of the two unknown angles has a lesser measure? What is the degree measure of this angle? • What is the degree measure of the remaining angle? Y 122° α
Transcribed Image Text:All values must be rounded off to 2 decimal places AND use these rounded off values when computing for other missing values. 1. Solve the triangle given below C 6 b B 4 A . b = • Based on the length of the sides opposite them, which of the two unknown angles has a lesser measure? What is the degree measure of this angle? • What is the degree measure of the remaining angle? Y 122° α
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
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