Answer: 5) 72.6° 6) 68.7° 7) 37.3° 8) 81.5°
Step-by-step explanation:
Law of Cosines: a² = b² + c² - 2bc · cos A
b² = a² + c² - 2ac · cos B
c² = a² + b² - 2ab · cos C
5) a = 27, b = 26, c = 20, A = ???
a² = b² + c² - 2bc · cos A
27² = 26² + 20² - 2(26)(20) · cos A
729 = 676 + 400 - 1040 cos A
729 = 1076 - 1040 cos A
-311 = -1040 cos A
[tex]\dfrac{311}{1040}=\cos A\\\\\cos^{-1}\bigg(\dfrac{311}{1040}\bigg)=A[/tex]
72.6° = A
6) a = 11, b = 13, c = 12, B = ???
b² = a² + c² - 2ac · cos B
13² = 11² + 12² - 2(11)(12) · cos B
169 = 121 + 144 - 264 cos B
169 = 265 - 264 cos B
-96 = -264 cos B
[tex]\dfrac{96}{264}=\cos B\\\\\cos^{-1}\bigg(\dfrac{96}{264}\bigg)=B[/tex]
68.7° = B
7) a = 19.2, b = 11.7, c = 16.5, B = ???
b² = a² + c² - 2ac · cos B
11.7² = 19.2² + 16.5² - 2(19.2)(16.5) · cos B
136.89 = 368.64 + 272.25 - 633.6 cos B
136.89 = 640.89 - 633.6 cos B
-504 = -633.6 cos B
[tex]\dfrac{504}{633.6}=\cos B\\\\\cos^{-1}\bigg(\dfrac{504}{633.6}\bigg)=B[/tex]
37.3° = B
8) a = 8.8, b = 12.4, c = 14.1, C = ???
c² = a² + b² - 2ab · cos C
14.1² = 8.8² + 12.4² - 2(8.8)(12.4) · cos C
198.81 = 77.44 + 153.76 - 218.24 cos C
198.81 = 231.2 - 218.24 cos C
-32.39 = -218.24 cos C
[tex]\dfrac{32.39}{218.24}=\cos C\\\\\cos^{-1}\bigg(\dfrac{32.39}{218.24}\bigg)=C[/tex]
81.5° = C
