A triangle has sides A, B, and C. The angle between sides A and B is $\frac{3 π}{4}$ $(3pi)/4$ . If side C has a length of $2$ $2$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , what are the lengths of sides A and B?

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Answer 1 · 2017-09-21T11:45:20

Length of sides $A and B$ $A and B$ are $0.73, 1.41$ $0.73 , 1.41$ unit respectively.

Angle between sides $A and B$ $A and B$ is $∠ c = \frac{3 π}{4} = \frac{3 \cdot 180}{4} = 135^{0}$ $/_c=(3pi)/4=(3*180)/4=135^0$

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

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

Length of side $C=2$ ; We know from sine law ,

$A/sin a = B/sin b = C/sin c :. B/sin30 = 2/sin135$

$:. B= 2* sin30/sin135 or B ~~ 1.41$ unit, similarly ,

$A/sin15 = 2/sin135 :. A = 2* sin15/sin135 or A ~~ 0.73$ unit.

Length of sides $A and B$ are $0.73 , 1.41$ unit respectively. [Ans]

A triangle has sides A, B, and C. The angle between sides A and B is (3pi)/43π4(3pi)/4. If side C has a length of 2 22 and the angle between sides B and C is pi/12π12pi/12, what are the lengths of sides A and B?