A triangle has sides A, B, and C. The angle between sides A and B is $(pi)/4$ . If side C has a length of $6$ 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 · 2018-02-28T12:06:33

Length of sides $A and B$ are $7.84 ,7.84$ unit respectively.

Angle between Sides $A and B$ is $/_c= pi/4=180/4=45^0$

Angle between Sides $B and C$ is $/_a= (3pi)/8=67.5^0 :.$

Angle between Sides $C and A$ is

$/_b= 180-(45+67.5)=67.5^0 ; C=6$

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:

$A/sinA = B/sinb=C/sinc ; C=6 :. B/sinb=C/sinc$ or

$B/sin67.5=6/sin45 or B= 6* (sin67.5/sin45) ~~ 7.84 (2dp)$

Similarly $A/sina=C/sinc:. A/sin67.5=6/sin 45$ or

$A= 6* (sin 67.5/sin45) ~~ 7.84 (2dp)$

Length of sides $A and B$ are $7.84 ,7.84$ unit respectively.[Ans]

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/4(pi)/4. If side C has a length of 6 6 and the angle between sides B and C is ( 3 pi)/8( 3 pi)/8, what are the lengths of sides A and B?