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 $9$ 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 · 2016-07-06T11:33:18

$A=9/2(sqrt(3)-1)$ ; $B=9/2sqrt(2)$

You can use the equation:

$A/sin hat(BC)=C/sin hat(AB)$

that, in this case, is:

$A/sin(pi/12)=9/sin(3pi/4)$

$A=9((sqrt(6)-sqrt(2))/4)/(sqrt(2)/2)$

$A=9((sqrt(6)-sqrt(2))/4)*2/sqrt(2)$

$A=9((sqrt(6)-sqrt(2))/(2sqrt(2)))$

$A=9(((sqrt(6)-sqrt(2))*sqrt(2))/(2sqrt(2)sqrt(2)))$

$A=9(sqrt(12)-2)/(4)$

$A=9/2(sqrt(3)-1)$

Now let's calculate $hat(AC)$ and B

$hat(AC)=pi-(pi/12+3pi/4)=pi/6$

$B/sin hat(AC)=C/sin(hat (AB))$

$B/sin (pi/6)=9/sin(3pi/4))$

$B=(9*1/2)/(sqrt(2)/2)=9/sqrt(2)=9/2sqrt(2)$

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 9 9 and the angle between sides B and C is pi/12pi/12, what are the lengths of sides A and B?