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 $\frac{π}{8}$ $( pi)/8$ , what are the lengths of sides A and B?

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Answer 1 · 2017-11-25T10:42:37

Length of sides $A and B$ $A and B$ are $0.44 and 1.14$ $0.44 and 1.14$ unit respectively.

Angle between Sides $A and B$ $A and B$ is $∠ c = \frac{π}{3} = \frac{180}{3} = 60^{0}$ $/_c= pi/3=180/3=60^0$

Angle between Sides $B and C$ $B and C$ is $/_a= pi/8=180/8=22.5^0 :.$

Angle between Sides $C and A$ is

$/_b= 180-(60+22.5)=97.5^0$

The sine rule states if $A, B and C$ are the lengths of the sides

and opposite angles are $a, b and c$ in a triangle, then:

$A/sina = B/sinb=C/sinc ; C=1 :. B/sinb=C/sinc$ or

$B/sin97.5=1/sin60 or B= 1* (sin97.5/sin60) ~~ 1.14 (2dp)$

Similarly $A/sina=C/sinc$ or

$A/sin22.5=1/sin60 or A= 1* (sin22.5/sin60) ~~ 0.44 (2dp)$

The length of sides $A and B$ are $0.44 and 1.14$ unit

respectively. [Ans]

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/3π3(pi)/3. If side C has a length of 1 11 and the angle between sides B and C is ( pi)/8π8( pi)/8, what are the lengths of sides A and B?