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

1 Answer
sankarankalyanam
Jun 21, 2018

#color(crimson)(c = 22.8 " units"#

Explanation:

#a = 12, b = 11,hat C= (11pi) / 12#

![http://www.mathwarehouse.com/trigonometry/http://law-of-cosines-formula-examples.php](https://useruploads.socratic.org/S4bT89y7TXOfTcfZc2al_Law%20of%20cosines.png)

Applying the Law of Cosines,

#c = sqrt(a^2 + b^2 - 2ab cos C)#

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

#color(crimson)(c = 22.8 " units"#

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