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 $14$ $14$ 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 $14$ $14$ 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 · 2017-02-14T18:03:47

a= 14.94 ; b=12.83

Explanation:

The measurements as given in the question are depicted in the figure below

: enter image source here

To determine sides 'a' and 'b', it is obvious that sine rule would be helpful here. Thus,
$\frac{sin A}{a} = \frac{sin B}{b} = \frac{sin C}{c}$ $sin A /a = sin B /b = Sin C/c$ . Here A is $\frac{3 π}{8}$ $(3pi)/8$ C is $\frac{π}{3}$ $pi/3$ and B is $(π - \frac{3 π}{8} - \frac{π}{3}) = \frac{7 π}{24}$ $(pi-(3pi)/8- pi/3) = (7pi)/24$

$\frac{sin (\frac{3 π}{8})}{a} = \frac{sin (\frac{7 π}{24})}{b} = \frac{sin (\frac{π}{3})}{14} = \frac{\sqrt{3}}{28}$ $(sin ((3pi)/8))/a= (sin ((7pi)/24))/b= sin(pi/3)/14=sqrt3/28$

$\frac{0.9238}{a} = \frac{0.7933}{b} = 0.0618$ $0.9238/a =0.7933/b= 0.0618$

This gives a= 14.94 ; b=12.83

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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 $14$ $14$ 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 1414 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 $14$ $14$ 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?