A triangle has sides A, B, and C. Sides A and B are of lengths $5$ $5$ and $2$ $2$ , respectively, and the angle between A and B is $\frac{5 π}{12}$ $(5pi)/12$ . What is the length of side C?

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A triangle has sides A, B, and C. Sides A and B are of lengths $5$ $5$ and $2$ $2$ , respectively, and the angle between A and B is $\frac{5 π}{12}$ $(5pi)/12$ . What is the length of side C?

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Answer 1 · 2016-03-28T22:33:10

Since the given information provided is the case Side-Angle-Side, you can apply the Law of Cosines to solve for the third side.

Explanation:

$c^{2} = 5^{2} + 2^{2} - 2 \cdot 5 \cdot 2 \cdot cos (\frac{5 \cdot π}{12})$ $c^2=5^2+2^2-2*5*2*cos((5*pi)/12)$
$c = \sqrt{5^{2} + 2^{2} - 2 \cdot 5 \cdot 2 \cdot cos (\frac{5 \cdot π}{12})}$ $c = sqrt(5^2+2^2-2*5*2*cos((5*pi)/12)$
$c = 4.88$ $c = 4.88$ units long.

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A triangle has sides A, B, and C. Sides A and B are of lengths $5$ $5$ and $2$ $2$ , respectively, and the angle between A and B is $\frac{5 π}{12}$ $(5pi)/12$ . What is the length of side C?

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A triangle has sides A, B, and C. Sides A and B are of lengths 55 and 22, respectively, and the angle between A and B is 5π12(5pi)/12 . What is the length of side C?

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A triangle has sides A, B, and C. Sides A and B are of lengths $5$ $5$ and $2$ $2$ , respectively, and the angle between A and B is $\frac{5 π}{12}$ $(5pi)/12$ . What is the length of side C?