SOLUTION: A triangle has sides of length 5cm, 6cm, and 9cm. calculate the value of angle x. (X is opposite the 6cm side) i dont know what equation to use

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Question 698758: A triangle has sides of length 5cm, 6cm, and 9cm.
calculate the value of angle x.

(X is opposite the 6cm side)
i dont know what equation to use
Found 2 solutions by vidya p, Edwin McCravy:
Answer by vidya p(12)   (Show Source): You can put this solution on YOUR website!
Solution:
LEt ABC is a triangle, with sides of measure, AB= c,AC = b,BC = a
the angle opposite of side 6 cm is x,
now to find the angle with the given three sides,
we can make use of the cosine rule which says that,
a^2 = b^2 + c^2 - 2bc cos (B)
6^2 = 9^2 + 5^2 - 2(9)(5)*cos x ,
36 = 81 + 25 - 90*cos (x)
36 - 106 = -90*cos(x)
-70 / -90 = cos (x)
x = arccos( 7/9)
Thanks
Best regards.
Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
This one for the case of SSS (all three sides known):

             (ONE SIDE OF ANGLE)²+(OTHER SIDE OF ANGLE)²-(OPPOSITE SIDE OF ANGLE)² 
cos(ANGLE) = ---------------------------------------------------------------------
                      2×(ONE SIDE OF ANGLE)×(OTHER SIDE OF ANGLE)


cos(x) = 

cos(x) = 

Work that out, then use the inverse cosine
feature on your calculator to get

x = 38.9424127 or 38°56'32.789"

Edwin
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