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

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Answer 1 · 2016-03-04T17:17:42

$c = \sqrt{a^{2} + b^{2} - 2 a b cos C} = \sqrt{4^{2} + 5^{2} - 2 (4) (5) cos (\frac{π}{8})} \approx 2.01$ $c=sqrt(a^2+b^2-2abcosC) = sqrt(4^2+5^2-2(4)(5)cos (pi/8) )~~ 2.01$

Explanation:

Use the law of cosines and then substitute in the values for a, b, and angle C and then find side c.

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A triangle has sides A, B, and C. Sides A and B are of lengths $4$ $4$ and $5$ $5$ , respectively, and the angle between A and B is $\frac{π}{8}$ $(pi)/8$ . 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 44 and 55, respectively, and the angle between A and B is π8(pi)/8 . 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 $4$ $4$ and $5$ $5$ , respectively, and the angle between A and B is $\frac{π}{8}$ $(pi)/8$ . What is the length of side C?