A triangle has sides A, B, and C. The angle between sides A and B is $(pi)/3$ . If side C has a length of $15$ and the angle between sides B and C is $( 3 pi)/8$ , what are the lengths of sides A and B?

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Answer 1 · 2016-01-24T12:33:03

side $a=16.0021$
side $b=13.7413$

To solve the triangle use the Sine Law
$a/sin A=b/sin B=c/sin C$

Compute angle B first using the formula $A+B+C=pi$

$B=pi-A-C$

$B=pi-(3pi)/8-pi/3$

$B=(7pi)/24$

Compute side a:

$a/sin A=c/sin C$

$a=(c*sin A)/sin C=15*sin ((3pi)/8)/(sin (pi/3))$

$a=16.0021$

Compute side b:

$b/sin B=c/sin C$

$b=(c*sin B)/sin C=15*sin ((7pi)/24)/(sin (pi/3))$

$b=13.7413$

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/3(pi)/3. If side C has a length of 15 15 and the angle between sides B and C is ( 3 pi)/8( 3 pi)/8, what are the lengths of sides A and B?