A triangle has sides A, B, and C. Sides A and B are of lengths #9# and #8#, respectively, and the angle between A and B is #(11pi)/12 #. What is the length of side C?

1 Answer
sankarankalyanam
Apr 8, 2018

#color(indigo)(c = 16.85 " units"#

Explanation:

![http://www.mathwarehouse.com/trigonometry/http://law-of-cosines-formula-examples.php](https://useruploads.socratic.org/gBzExigTTlasjX9KtHpo_law%20of%20cosines.png)

As per the Law of Cosines,

#c^2 = a ^2 + b^2 - 2 * a * b * cos C#

#c^2 = 9^2 + 8^2 - 2 * 9 * 8 * cos ((11pi)/12)#

#c^2 = 81 + 64 + 144 cos (pi/12), " as " cos (pi - theta) = - cos theta#

#c^2 = 145 + 144 cos (pi/12) = 284.09#

#c = +- sqrt (284.09) = 16.85#

As c cannot be negative, #color(indigo)(c = 16.85 " units"#

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