A triangle has sides A, B, and C. Sides A and B are of lengths 11 and 12, respectively, and the angle between A and B is (5pi)/8 . What is the length of side C?

1 Answer
Jim G.
Apr 12, 2016

≈ 19.13

Explanation:

In a triangle , given 2 sides and the angle between them, to find the 3rd side use the color(blue)" cosine rule "

color(red)(|bar(ul(color(white)(a/a)color(black)( c^2 = a^2 + b^2 - (2abcosC))color(white)(a/a)|)))

where a , b are the 2 known sides and angle C , is the angle between them.
here a = 11 , b = 12 and angle C = (5pi)/8

substituting these values into the formula

c^2 = 11^2 + 12^2 - ( 2xx11xx12xxcos((5pi)/8) )

= 121 + 144 - ( -101.03) = 366.03

now c^2 = 366.03 rArr c = sqrt366.03 ≈ 19.13

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