A triangle has sides A, B, and C. Sides A and B are of lengths #1# and #2#, respectively, and the angle between A and B is #(pi)/8 #. What is the length of side C?

1 Answer
maganbhai P.
Feb 26, 2018

Answer for the updated question given below.
#c~~1.14#

Explanation:

#color(red)( triangle ABC)# has sides#color(red)(AB, BC,and CA#. Sides #color(red)(a)# and #color(red)(b)# are of lengths 1 and 2 respectively, and the angle between #color(red)(a)# and #color(red)(b)# is #pi/8#. What is the length of side #color(red)(c)#?
Where#color(red)(AB=c,BC=a and CA=b.)#
Here, #a=1,b=2,C=pi/8#
Using the Law of Cosines:
#cosC=(a^2+b^2-c^2)/(2ab) rArrc^2=a^2+b^2-2abcosC#
Hence,#c^2=(1)^2+(2)^2-2(1)(2)cos(pi/8) ~~1+4-4(0.9239) rArr c^2~~5-3.6956=1.3044##color(red)(rArrc~~1.14)#

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