A triangle has sides A, B, and C. Sides A and B are of lengths #7# and #5#, respectively, and the angle between A and B is #(pi)/8 #. What is the length of side C?

1 Answer
Jim G.
Sep 29, 2016

#≈3.054" units"#

Explanation:

Given a triangle, where 2 sides and the angle between them are known, in this case A and B and we wish to calculate the length of the third side C, use the #color(blue)"cosine rule"#

#color(red)(bar(ul(|color(white)(a/a)color(black)(C^2=A^2+B^2-(2ABcos("angle between them")))color(white)(a/a)|)))#

here A = 7 , B = 5 and angle between them #=pi/8#

substitute these values into the 'cosine rule'

#C^2=7^2+5^5-(2xx7xx5xxcos(pi/8))#

#=49+25-(64.672...)#

#=74-(64.672...)≈9.328#

Now # C^2≈9.328rArrC=sqrt(9.328)≈3.054#

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