A triangle has sides A, B, and C. Sides A and B are of lengths $7$ $7$ and $2$ $2$ , respectively, and the angle between A and B is $\frac{3 π}{8}$ $(3pi)/8$ . What is the length of side C?

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Answer 1 · 2018-02-25T13:56:10

Length of side $c = 5$ $color(purple)(c = 5$

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Given : $a = 7, b = 2, ˆ C = \frac{3 π}{8}$ $a = 7, b = 2, hatC = (3pi)/8$

$a a a a a a a a a a a$ $color(white)(aaaaaaaaaaa)$ Applying Law of Cosines

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

$c^{2} = 7^{2} + 2^{2} - (2 \cdot 7 \cdot 2 \cdot cos (\frac{3 π}{8}) = 25$ $c^2 = 7^2 + 2^2 - (2 *7*2*cos((3pi)/8) = 25$

$c = 5$ $c = 5$

A triangle has sides A, B, and C. Sides A and B are of lengths 77 and 22, respectively, and the angle between A and B is 3π8(3pi)/8 . What is the length of side C?