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 $15$ $15$ 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 · 2016-01-24T12:33:03

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

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

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

$B = π - A - C$ $B=pi-A-C$

$B = π - \frac{3 π}{8} - \frac{π}{3}$ $B=pi-(3pi)/8-pi/3$

$B = \frac{7 π}{24}$ $B=(7pi)/24$

Compute side a:

$\frac{a}{sin A} = \frac{c}{sin C}$ $a/sin A=c/sin C$

$a = \frac{c \cdot sin A}{sin C} = 15 \cdot \frac{sin (\frac{3 π}{8})}{sin (\frac{π}{3})}$ $a=(c*sin A)/sin C=15*sin ((3pi)/8)/(sin (pi/3))$

$a = 16.0021$ $a=16.0021$

Compute side b:

$\frac{b}{sin B} = \frac{c}{sin C}$ $b/sin B=c/sin C$

$b = \frac{c \cdot sin B}{sin C} = 15 \cdot \frac{sin (\frac{7 π}{24})}{sin (\frac{π}{3})}$ $b=(c*sin B)/sin C=15*sin ((7pi)/24)/(sin (pi/3))$

$b = 13.7413$ $b=13.7413$

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 1515 and the angle between sides B and C is 3π8( 3 pi)/8, what are the lengths of sides A and B?