A triangle has sides A, B, and C. Sides A and B are of lengths $2$ $2$ and $3$ $3$ , 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 $2$ $2$ and $3$ $3$ , 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 · 2016-02-05T19:30:24

C ≈ 3.15

Explanation:

In this question since 2 sides A and B of the triangle are known as is the angle between them then use

$cosine Rule stated below$ $color(blue)(" Cosine Rule ") color(black)(" stated below ")$

for this triangle :

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

where $θ is angle between A and B$ $theta color(black)(" is angle between A and B")$

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

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

$\Rightarrow C^{2} = 4 + 9 - (12 \times cos (\frac{5 π}{12}) \approx 9.9$ $rArr C^2 = 4+9 - (12 xx cos((5pi)/12) ≈9.9$

( remember this is $C^{2})$ $C^2 )$

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

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A triangle has sides A, B, and C. Sides A and B are of lengths $2$ $2$ and $3$ $3$ , 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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Explanation:

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A triangle has sides A, B, and C. Sides A and B are of lengths 222 and 333, 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 $2$ $2$ and $3$ $3$ , respectively, and the angle between A and B is $\frac{5 π}{12}$ $(5pi)/12$ . What is the length of side C?