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

 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

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

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

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

19.7° = A

hey seth! : )

i’m not 100% sure, but i think it’s b

hope this ya : p

miss u!

- nicole

starting with:    

5 + x - 12 = 2x - 7   

5 + x - 12 - x = 2x - 7 - x (subtract x from both sides)   

5 - 12 = x - 7 (combine and cancel x's from both sides)   

5 - 12 + 7 = x - 7 + 7 (add 7 to both sides)   

0 = x (add numbers together on both sides)       

so in order for the equation to be true, x must be 0.   

trying x = -0.5   

5 + x - 12 = 2x - 7 (original equation)   

5 + -0.5 - 12 = 2(-0.5) - 7 (plug in value of x)   

5 + -0.5 - 12 = -1 - 7 (did multiplication)   

-7.5 = -8 (did addition on both sides)       

since -7.5 is obviously not equal to -8, the value of -0.5 for x is wrong.   

trying x = 0   

5 + x - 12 = 2x - 7 (original equation)   

5 + 0 - 12 = 2(0) - 7 (plug in value of x)   

5 + 0 - 12 = 0 - 7 (did multiplication)   

-7 = -7 (did addition on both sides)       

since -7 equals -7, that demonstrates that the value of 0 for x is correct.   

trying x = 1   

5 + x - 12 = 2x - 7 (original equation)   

5 + 1 - 12 = 2(1) - 7 (plug in value of x)   

5 + 1 - 12 = 2 - 7 (did multiplication)   

-6 = -5 (did addition on both sides)       

since -6 is obviously not equal to -5, the value of 1 for x is wrong.