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 $15$ $15$ 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 · 2018-01-12T10:35:07

The length of sides $A and B$ $A and B$ are $5.49 and 10.61$ $5.49 and 10.61$ 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 $∠ a = \frac{π}{12} = \frac{180}{12} = 15^{0}$ $/_a= pi/12=180/12=15^0$

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

The sine rule states if $A, B and C$ $A, B and C$ are the lengths of the sides

and opposite angles are $a, b and c$ $a, b and c$ in a triangle, then:

$A/sina = B/sinb=C/sinc ; C=15 :. B/sinb=C/sinc$ or

$B/sin30=15/sin135 or B= 15* (sin30/sin135) ~~ 10.61 (2dp)$

Similarly $A/sina=C/sinc$ or

$A/sin15=15/sin135 or A= 15* (sin15/sin135) ~~ 5.49 (2dp)$

The length of sides $A and B$ are $5.49 and 10.61$ 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 15 1515 and the angle between sides B and C is pi/12π12pi/12, what are the lengths of sides A and B?