A triangle has sides A, B, and C. Sides A and B are of lengths #1# and #3#, respectively, and the angle between A and B is #(pi)/8 #. What is the length of side C?

1 Answer

Answer:

#c=sqrt(10-6cos(pi/8))=sqrt(10-3*sqrt(2+sqrt2))#

#c=2.1111# units

Explanation:

By the #color (blue)"Cosine law"# the side third side can readily computed when #color (blue) "two sides and an included angle are given"#

#a=1# and #b=3# and angle #C=pi/8#

#c=sqrt(a^2+b^2-2*a*b*cos C)#

#c=sqrt(1^2+3^2-2*1*3*cos(pi/8))#

#c=sqrt(10-6*cos(pi/8))# and #cos(pi/8)=1/2sqrt(2+sqrt2)#

#c=2.1111 #units

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