A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{6}$ $(5pi)/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 7, what is the area of the triangle?

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{6}$ $(5pi)/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 7, what is the area of the triangle?

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Answer 1 · 2016-05-07T11:09:22

The Area is $12.25$ $12.25$ square units

Explanation:

The angle between sides A and B $∠ C = 5 \cdot \frac{180}{6} = 150^{0}$ $/_C= 5*180/6=150^0$
The angle between sides B and C $∠ A = \frac{180}{12} = 15^{0}$ $/_A= 180/12=15^0$
The angle between sides C and A $∠ B = 180 - (150 + 15) = 15^{0}$ $/_B= 180-(150+15)=15^0$
By sine law , we know $A/sinA=B/sinB=C/sinC :. A=SinA/sinB*B=7*sin15/sin15=7$ Now $A=7 ; B=7$ and their included angle $/_C=150^0 :.$ The Area $=A*B*sinC/2=7*7*sin150/2 =12.25$ square units[Ans}

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{6}$ $(5pi)/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 7, what is the area of the triangle?

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Explanation:

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1 Answer

Explanation:

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{5 π}{6}$ $(5pi)/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 7, what is the area of the triangle?