A triangle has sides A, B, and C. Sides A and B are of lengths #6# and #8#, respectively, and the angle between A and B is #(5pi)/8 #. What is the length of side C?

1 Answer
Jim G.
Apr 15, 2016

≈ 11.69

Explanation:

Given a triangle with 2 sides and the angle between them known.
Then to find the third side we use the#color(blue)" cosine rule " #

#color(red)(|bar(ul(color(white)(a/a)color(black)( c^2 = a^2 + b^2 - (2ab costheta)color(white)(a/a)|)))#
where a , b are the 2 known sides , #theta" is the angle between them and c is the side to be found "#

here a = 6 , b = 8 and #theta = (5pi)/8 #

substitute these values into the formula.

#c^2 = 6^2 + 8^2 - (2xx6xx8xxcos((5pi)/8) ) #

= 36 + 64 - ( -36.738) = 136.738

now #c^2 = 136.738 rArr c = sqrt136.738 ≈ 11.69 #

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