A triangle has sides A, B, and C. Sides A and B are of lengths $14$ $14$ and $12$ $12$ , respectively, and the angle between A and B is $\frac{5 π}{8}$ $(5pi)/8$ . 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 $14$ $14$ and $12$ $12$ , respectively, and the angle between A and B is $\frac{5 π}{8}$ $(5pi)/8$ . What is the length of side C?

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Answer 1 · 2016-03-10T14:35:03

≈ 21.647 units

Explanation:

Given a triangle with 2 sides and the angle between them known, find the 3rd side using the $cosine rule$ $color(blue)" cosine rule "$

$c^{2} = a^{2} + b^{2} - (2 a b cos θ)$ $c^2 = a^2 + b^2 - (2ab costheta)$

where c is the side to be found , a and b are the known sides and $θ is the angle between them$ $theta " is the angle between them "$

here a = 14 , b = 12 and $θ = \frac{5 π}{8}$ $theta = (5pi)/8$

hence $c^{2} = 14^{2} + 12^{2} - (2 \times 14 \times 12 cos (\frac{5 π}{8}))$ $c^2 = 14^2 + 12^2 -( 2xx14xx12 cos((5pi)/8))$

$= 196+144 + 128.582...$ ≈ 468.582

$rArr c = sqrt468.582 ≈ 21.647 " units "$

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A triangle has sides A, B, and C. Sides A and B are of lengths $14$ $14$ and $12$ $12$ , respectively, and the angle between A and B is $\frac{5 π}{8}$ $(5pi)/8$ . What is the length of side C?

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Explanation:

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A triangle has sides A, B, and C. Sides A and B are of lengths 141414 and 121212, respectively, and the angle between A and B is (5pi)/8 5π8(5pi)/8 . What is the length of side C?

1 Answer

Explanation:

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A triangle has sides A, B, and C. Sides A and B are of lengths $14$ $14$ and $12$ $12$ , respectively, and the angle between A and B is $\frac{5 π}{8}$ $(5pi)/8$ . What is the length of side C?