Answer: (7) 7.0 (8) 17.3 (9) 64.7°
Step-by-step explanation:
Law of Cosines is: a² = b² + c² - 2bc · cos A
or: b² = a² + c² - 2ac · cos B
or: c² = a² + b² - 2ab · cos C
7) b = 4, c = 10, ∠A = 34
a² = b² + c² - 2bc · cos A
= 4² + 10² - 2(4)(10) · cos 34°
= 16 + 100 - 80 (0.829)
= 116 - 66.323
= 49.677
a = [tex]\sqrt{49.677}[/tex]
a = 7.0
8) a = 11, b = 8, ∠C = 131
c² = a² + b² - 2ab · cos C
= 11² + 8² - 2(11)(8) · cos 131°
= 121 + 64 - 176 (-0.656)
= 185 + 115
= 300
c = [tex]\sqrt{300}[/tex]
c = 17.3
9) a = 10.5, b = 5.9, c = 9.6
9.6² = 10.5² + 5.9² - 2(10.5)(5.9) · cos C
92.16 = 110.25 + 34.81 - 2(10.5)(5.9) · cos C
92.16 = 145.06 - 123.9 cos C
-52.9 = -123.9 cos C
0.427 = cos C
cos⁻¹ (0.427) = C
64.7° = C
