A triangle has sides A, B, and C. The angle between sides A and B is $(3pi)/4$ . If side C has a length of $5$ and the angle between sides B and C is $pi/12$ , what are the lengths of sides A and B?

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Answer 1 · 2017-10-01T12:59:22

The lengths of sides $A and B$ are $1.83 ,3.54$ unit respectively.

Angle between Sides $A and B$ is $/_c= (3pi)/4=(3*180)/4=135^0$

Angle between Sides $B and C$ is $/_a= pi/12=180/12=15^0 :.$

Angle between Sides $C and A$ is $/_b= 180-(135+15)=30^0$

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:

$A/sinA = B/sinb=C/sinc ; C=5 :. B/sinb=C/sinc$ or

$B/sin30=5/sin135 or B= 5* (sin30/sin135) ~~ 3.54 (2dp)$

Similarly $A/sina=C/sinc$ or

$A/sin15=5/sin135 or A= 5* (sin15/sin135) ~~ 1.83 (2dp)$

The length of sides $A and B$ are $1.83 ,3.54$ unit respectively.

[Ans]

A triangle has sides A, B, and C. The angle between sides A and B is (3pi)/4(3pi)/4. If side C has a length of 5 5 and the angle between sides B and C is pi/12pi/12, what are the lengths of sides A and B?