A triangle has sides A, B, and C. Sides A and B are of lengths $5$ $5$ and $3$ $3$ , 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 · 2018-04-02T06:36:17

$c = \sqrt{6.2836} \approx 2.5 units$ $color(purple)(c = sqrt(6.2836) ~~ 2.5 " units"$

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Given $a = 5, b = 3, ˆ C = \frac{π}{8}$ $a = 5, b = 3, hat C = pi/8$ , To find side c.

$c^{2} = a^{2} + b^{2} - (2 a b cos C)$ $c^2 = a ^2 + b^2 - (2 a b cos C)$

$c^{2} = 5^{2} + 3^{2} - (2 \cdot 5 \cdot 3 \cdot cos (\frac{π}{8})) = 6.2836$ $c^2 = 5^2 + 3^2 - (2 * 5 * 3 * cos (pi/8) )= 6.2836$

$c = \sqrt{6.2836} = 2.5 units$ $color(purple)(c = sqrt(6.2836) = 2.5 " units"$

A triangle has sides A, B, and C. Sides A and B are of lengths 555 and 333, respectively, and the angle between A and B is (pi)/8 π8(pi)/8 . What is the length of side C?