Answer: 17) 41.0° 18) 60.8° 19) 36.0° 20) 19.7°
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
17) a = 29, b = 13, c = 21, C = ???
c² = a² + b² - 2ab · cos C
21² = 29² + 13² - 2(29)(13) · cos C
441 = 841 + 169 - 754 cos C
441 = 1010 - 754 cos C
-569 = -754 cos C
[tex]\dfrac{569}{754}=\cos C\\\\\cos^{-1}\bigg(\dfrac{569}{754}\bigg)=C[/tex]
41.0° = C
18) a = 29.3, b = 25.7, c = 16.8, B = ???
b² = a² + c² - 2ac · cos B
25.7² = 29.3² + 16.8² - 2(29.3)(16.8) · cos B
660.49 = 858.49 + 282.24 - 984.48 cos B
660.49 = 1140.73 - 984.48 cos B
-480.24 = -984.48 cos B
[tex]\dfrac{480.24}{984.48}=\cos B\\\\\cos^{-1}\bigg(\dfrac{480.24}{984.48}\bigg)=B[/tex]
60.8° = B
19) a = 12, b = 19, c = 11, A = ???
a² = b² + c² - 2bc · cos A
12² = 19² + 11² - 2(19)(11) · cos A
144 = 361 + 121 - 418 cos A
144 = 482 - 418 cos A
-338 = -418 cos A
[tex]\dfrac{338}{418}=\cos A\\\\\cos^{-1}\bigg(\dfrac{338}{418}\bigg)=A[/tex]
36.0° = A
20) a = 10, b = 9, c = 18, A = ???
a² = b² + c² - 2bc · cos A
100² = 9² + 18² - 2(9)(18) · cos A
100 = 81 + 324 - 324 cos A
100 = 405 - 324 cos A
-305 = -324 cos A
[tex]\dfrac{305}{324}=\cos A\\\\\cos^{-1}\bigg(\dfrac{305}{324}\bigg)=A[/tex]
19.7° = A
