How do you solve the triangle given a = 4, b = 5, and c = 6?

1 Answer
sankarankalyanam
Jun 21, 2018

#color(indigo)(hat A = 41.41^@, hat B = 55.77^@, hat C = 82.82^@#

Explanation:

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

#a = 4, b = 5, c = 6#

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

#hat C = cos^-1 ((4^2 + 5^2 - 6^2) / (2 * 4 * 5))= 82.82^@#

#hat B = cos^-1 ((4^2 + 6^2 - 5^2) / (2 * 4 * 6))= 55.77^@#

#hat A = 180 - 82.82 - 55.77 = 41.41^@#

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