A triangle has sides A, B, and C. Sides A and B are of lengths #7# and #6#, respectively, and the angle between A and B is #(pi)/8 #. What is the length of side C?

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Answer 1 · 2018-04-16T11:16:31

#2.719 units# to 3 decimal places

#pi/8xx180/pi=22.5^@=22^@30'#

Use the cosine rule:-

#:.c^2=a^2+b^2-2abcosC#

#:.c^2=7^2+6^2-2abcos22^@30'#

#:.c^2=49+36-(2*7*6*0.0923879532)#

#:.c^2=49+36-(77.60588076)#

#:.c^2=7.39411924#

#:.sqrt(c^2)=sqrt(7.39411924)#

#:.c=2.719212982#

#:.c=2.719 units# to 3 decimal places