A triangle has sides A, B, and C. Sides A and B are of lengths $4$ and $9$ , respectively, and the angle between A and B is $(5pi)/8$ . What is the length of side C?

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Answer 1 · 2018-03-13T07:41:50

$c=11.2$

Well, this is a classic use of the cosine rule

$c^2=a^2+b^2-2abcos(C)$

$c^2=(4)^2+(9)^2-2(4)(9)cos((5pi)/8)$

$c^2=16+81-72(-0.382683)$

$c^2=124.553$

$c=sqrt(124.553)$

$c=11.2$

A triangle has sides A, B, and C. Sides A and B are of lengths 44 and 99, respectively, and the angle between A and B is (5pi)/8 (5pi)/8 . What is the length of side C?