SOLUTION: Triangle ABC has AB= 7 cm, AC = 13, BC = x cm and angle ABC = 60 degrees. Calaculate the exact value of x

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Question 1114003: Triangle ABC has AB= 7 cm, AC = 13, BC = x cm and angle ABC = 60 degrees. Calaculate the exact value of x
Found 2 solutions by rothauserc, ikleyn:
Answer by rothauserc(4718)   (Show Source):
You can put this solution on YOUR website!
use the law of cosines
:
13^2 = 7^2 +x^2 - 7 * x * cos(60)
:
169 = 49 +x^2 - 7x * (1/2)
:
x^2 -3.5x -120 = 0
:
use the quadratic formula
:
x = (-(-3.5) +square root((-3.5)^2-4*1*(-120))) / (2 * 1) = 12.8434
:
x = (-(-3.5) -square root((-3.5)^2-4*1*(-120))) / (2 * 1) = −9.3434
:
reject negative value for x
:
x = 12.8434 cm
:

Answer by ikleyn(52781)   (Show Source):
You can put this solution on YOUR website!
.

= 169 = 49 + , = 0 (x-15)*(x+8) = 0 We are looking for the positive root, therefore, the only solution is x= 15.

Answer.   x = 15.