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)/8 #. What is the length of side C?

1 Answer
Dec 19, 2016

Answer:

c=5.8737

Explanation:

The figure explaining the given data is given below:
enter image source here

To find side 'c', Cosine rule would apply in this case. Cosine rule says that

Cos C= #(a^2+b^2-c^2)/(2ab)#. Plugging in the given values, it would be

#Cos ((7pi)/8) =(4+16-c^2)/16 #

#c^2= 20-16cos( (7pi)/8)= 20- 16cos (pi-pi/8)= 20+16cos (pi/8)= 20+14.5009= 34.5009#

c=5.8737