SOLUTION: Find the missing parts using the Cosine Law. a = ? A = 40º b = 8 B = ? c = 10 C

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Question 829942: Find the missing parts using the Cosine Law.
a = ? A = 40º
b = 8 B = ?
c = 10 C = ?

Answer by math-vortex(648) About Me  (Show Source):
You can put this solution on YOUR website!
Hi, there--

THE PROBLEM:
Find the missing parts using the Cosine Law:
a =   ?     A =  40º            
b =   8    B =   ?             
c =   10  C =   ?    

A SOLUTION:
The Cosine Rule can be written in three forms:

a%5E2=b%5E2%2Bc%5E2-2bc%2Acos%28A%29
b%5E2=a%5E2%2Bc%5E2-2ac%2Acos%28B%29
c%5E2=a%5E2%2Bb%5E2-2ab%2Acos%28C%29

Use the first form to solve for a
a%5E2=b%5E2%2Bc%5E2-2bc%2Acos%28A%29
a%5E2=%288%29%5E2%2B%2810%29%5E2-2%288%29%2810%29%2Acos%2840%29
a%5E2=64%2B100-160%2A%280.7760%29
a%5E2=41.4329
a=6.4

Use the second form to solve for angle B.
b%5E2=a%5E2%2Bc%5E2-2ac%2Acos%28B%29
%288%29%5E2=%2841.4329%29%2B%2810%29%5E2-2%286.4%29%2810%29%2Acos%28B%29
64=41.4329%2B100-128%2Acos%28B%29
cos%28B%29=-77.4329%2F-128=0.6049
B=52.8

Use the third form to solve for angle C.
c%5E2=a%5E2%2Bb%5E2-2ab%2Acos%28C%29
%2810%29%5E2=%2841.4329%29%2B%288%29%5E2-2%286.4%29%288%29%2Acos%28C%29
100=41.4329%2B64-102.4%2Acos%28C%29
cos%28C%29=-5.4329%2F-102.4=-0.6049
C=87.0


a = 6.4  A =  40º            
b = 8    B =   52.8º             
c = 10  C =   87.0º    

These values are approximate, rounded to the tenths place.

Hope this helps! Feel free to email if you have any questions about the solution.

Good luck with your math,

Mrs. F
math.in.the.vortex@gmail.com