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Please find a and include all steps. 

 Jul 12, 2021
 #1
avatar
-2

By the Cosines Law, a = 5 + sqrt(41).

 Jul 12, 2021
 #2
avatar+32633 
+2

The cosine rule here can be written as:

 

12^2 = a^2 + 10^2 - 2*a*10*cos(60deg)

 

or  a^2 - 20*cos(60deg)*a - 44 = 0

 

solve the quadratic equation to find a.

 Jul 12, 2021
edited by Alan  Jul 12, 2021
 #3
avatar+35057 
+2

Using Law of Sines

 

sin 60 / 12 = sin b / 10

b = 46.194 degrees

 

angle A = 180 - 46.194 - 60 = 73.8059 degrees

 

12 / sin 60 = a / sin 73.8059

a = 13.31 units

 Jul 12, 2021
 #4
avatar+1540 
+2

Height    AD = sin60 * 10 

CD = cos60 * 10

BD = sqrt(AB2 - AD2)

a = CD + BD 

 

 Jul 12, 2021

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