Question

Part 5. Use the laws of sines. Please show work. Round to the nearest tenth.​

Answer 1

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

$\dfrac{569}{754}=\cos C\\\\\cos^{-1}\bigg(\dfrac{569}{754}\bigg)=C$

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

$\dfrac{480.24}{984.48}=\cos B\\\\\cos^{-1}\bigg(\dfrac{480.24}{984.48}\bigg)=B$

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

$\dfrac{338}{418}=\cos A\\\\\cos^{-1}\bigg(\dfrac{338}{418}\bigg)=A$

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

$\dfrac{305}{324}=\cos A\\\\\cos^{-1}\bigg(\dfrac{305}{324}\bigg)=A$

19.7° = A

Answer 2

Answer:

7) 41.0°      18) 60.8°       19) 36.0°        20) 19.7°

Step-by-step explanation: