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 $18$ 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 · 2017-09-26T11:13:19

Lengths of sides $A and B$ are $23.52$ unit each.

The angle between sides $A and B$ is $/_c =pi/4 = 180/4=45^0$

Angle between sides $B and C$ is $/_a =(3pi)/8=(3*180)/8=67.5^0$

Angle between sides $C and A$ is

$/_b=180-(45+67.5)= 67.5^0 : C =18$ We know by sine rule

$A/sina=B/sinb=C/sinc :. A= C* sina/sinc =18 * sin67.5/sin 45$

$:.A ~~ 23.52(2dp)$ , similarly $B= C* sinb/sinc =18 * sin67.5/sin 45$

$:.B ~~ 23.52 (2dp)$ . Lengths of $A and B$ are $23.52$ unit each. [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 18 18 and the angle between sides B and C is ( 3 pi)/8( 3 pi)/8, what are the lengths of sides A and B?