A triangle has sides A, B, and C. Sides A and B are of lengths $3$ $3$ 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 $3$ $3$ 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 · 2016-02-13T20:54:18

C ≈ 3.15

Explanation:

In this triangle , 2 sides and the angle between them are known.In this situation to solve for C use $cosine rule$ $color(blue)(" cosine rule ")$

for this triangle the cosine rule is

$C^{2} = A^{2} + B^{2} - (2 A B cos θ)$ $C^2 = A^2 + B^2 - (2ABcostheta)$

here A = 3 , B = 2 and $θ = \frac{5 π}{12}$ $theta = (5pi)/12$
substitute these values into formula

$C^{2} = 3^{2} + 2^{2} - (2 \times 3 \times 2 cos (\frac{5 π}{12})$ $C^2 = 3^2 + 2^2 - ( 2 xx 3 xx2cos((5pi)/12 )$

= 9+4 - 3.1 = 13 - 3.1 = 9.9

$C^{2} = 9.9 \Rightarrow C = \sqrt{9.9} \approx 3.15$ $C^2 = 9.9 rArr C = sqrt9.9 ≈ 3.15$

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A triangle has sides A, B, and C. Sides A and B are of lengths $3$ $3$ 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 333 and 222, respectively, and the angle between A and B is (5pi)/12 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 $3$ $3$ 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?