A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{3}$ $(pi)/3$ . If side C has a length of $1$ $1$ and the angle between sides B and C is $\frac{3 π}{8}$ $( 3 pi)/8$ , what are the lengths of sides A and B?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{3}$ $(pi)/3$ . If side C has a length of $1$ $1$ and the angle between sides B and C is $\frac{3 π}{8}$ $( 3 pi)/8$ , what are the lengths of sides A and B?

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Answer 1 · 2016-01-21T17:11:25

$A = C \frac{sin a}{sin c}$ $A = C sina/sinc$
$A = \frac{\sqrt{6 + 3 \sqrt{2}}}{3}$ $A =sqrt(6+3sqrt(2))/3$

And B Can be calculated as

$B = C \frac{sin b}{sin c} = \frac{sin (\frac{7}{24} π)}{\frac{\sqrt{3}}{2}}$ $B = C sinb/sinc= sin(7/24pi)/(sqrt(3)/2)$

Explanation:

Use sin law:
$\frac{A}{sin a} = \frac{C}{sin c} = \frac{B}{sin b}$ $A/sina = C/sinc = B/sinb$
$A = C \frac{sin a}{sin c}$ $A = C sina/sinc$ now we know $c = \frac{π}{3}; C = 1; a = \frac{3}{8} π; b = \frac{7}{24} π$ $c=pi/3; C=1; a=3/8pi; b=7/24pi$
so $A = \frac{1}{2} \frac{\sqrt{2 + \sqrt{2}}}{\frac{\sqrt{3}}{2}}$ $A = 1/2 sqrt(2+sqrt(2))/(sqrt(3)/2)$
$A = \frac{\sqrt{6 + 3 \sqrt{2}}}{3}$ $A = sqrt(6+3sqrt(2))/3$
And B
Can be calculated as
$B = C \frac{sin b}{sin c} = \frac{sin (\frac{7}{24} π)}{\frac{\sqrt{3}}{2}}$ $B = C sinb/sinc= sin(7/24pi)/(sqrt(3)/2)$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{3}$ $(pi)/3$ . If side C has a length of $1$ $1$ and the angle between sides B and C is $\frac{3 π}{8}$ $( 3 pi)/8$ , what are the lengths of sides A and B?

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A triangle has sides A, B, and C. The angle between sides A and B is π3(pi)/3. If side C has a length of 11 and the angle between sides B and C is 3π8( 3 pi)/8, what are the lengths of sides A and B?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{3}$ $(pi)/3$ . If side C has a length of $1$ $1$ and the angle between sides B and C is $\frac{3 π}{8}$ $( 3 pi)/8$ , what are the lengths of sides A and B?