A triangle has sides A, B, and C. Sides A and B are of lengths $5$ and $4$ , respectively, and the angle between A and B is $(7pi)/12$ . What is the length of side C?

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Answer 1 · 2015-12-31T02:20:49

$c ~= 7.166$

By the Law of Cosines: $c^2 = a^2 + b^2 - 2ab cos(Theta)$
In this example $a=5, b=4, Theta = (7 pi)/12$

Hence $c^2 = 5^2 + 4^2 - 2. 5. 4 cos((7 pi)/12)$
$c^2 = 25 + 16 - 40 cos((7 pi)/12)$

Using a calculator $cos((7 pi)/12) ~= -0.2588190451$

Therefore $c^2 ~= 41 + 40 * 0.2588190451$

$c^2 ~= 51.3527616$
$c ~= +-sqrt(51.3527616)$

Since c must be positive
$c = 7.166$ To 3 decimal places

A triangle has sides A, B, and C. Sides A and B are of lengths 55 and 44, respectively, and the angle between A and B is (7pi)/12 (7pi)/12 . What is the length of side C?