A triangle has sides A, B, and C. Sides A and B are of lengths #2# and #4#, respectively, and the angle between A and B is #(7pi)/12 #. What is the length of side C?

1 Answer
sankarankalyanam
Jun 5, 2018

Length of third side #color(brown)(c = 4.91# units

Explanation:

#a = 2, b = 4, hat C = (7pi)/12, c = ?

Applying the Law of Cosines,

![https://www.onlinemathlearning.com/http://law-of-cosines.html](https://useruploads.socratic.org/i5fQNJSSyOHutlTiFGdg_cosine%20law.png)

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

#c = sqrt (2^2 + 4^2 - (2 * 2 * 4* cos ((7pi)/12))#

Length of third side #color(brown)(c = 4.91# units

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