Question

Find the indicated angle. Round your answer to the nearest tenth. Part 2. Show work please​

Answer 1

Answer: 5) 72.6° 6) 68.7° 7) 37.3° 8) 81.5°

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

`(311)/(1040)=\cos A\\\\\cos^(-1)\bigg((311)/(1040)\bigg)=A`

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

`(96)/(264)=\cos B\\\\\cos^(-1)\bigg((96)/(264)\bigg)=B`

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

`(504)/(633.6)=\cos B\\\\\cos^(-1)\bigg((504)/(633.6)\bigg)=B`

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

`(32.39)/(218.24)=\cos C\\\\\cos^(-1)\bigg((32.39)/(218.24)\bigg)=C`

81.5° = C