A triangle has sides A, B, and C. The angle between sides A and B is $\frac{7 π}{12}$ $(7pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 26, 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 $\frac{7 π}{12}$ $(7pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 26, what is the area of the triangle?

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Answer 1 · 2017-08-05T10:33:20

$area \approx 97.568 square units$ $"area "~~ 97.568" square units"$

Explanation:

$calculate the area ( A ) of the triangle using$ $"calculate the area ( A ) of the triangle using"$

$∙ x A = \frac{1}{2} A B sin C$ $•color(white)(x)A=1/2ABsinC$

$where C is the angle between sides A and B$ $"where C is the angle between sides A and B"$

$we require to calculate the side A$ $"we require to calculate the side A"$

$the third angle in the triangle is$ $" the third angle in the triangle is"$

$π - (\frac{7 π}{12} + \frac{π}{12}) = \frac{π}{3}$ $pi-((7pi)/12+pi/12)=pi/3$

$using the sine rule$ $"using the "color(blue)"sine rule "$ in triangle ABC

$\frac{A}{sin (\frac{π}{12})} = \frac{26}{sin (\frac{π}{3})}$ $A/sin(pi/12)=26/sin(pi/3)$

$\Rightarrow A = \frac{26 sin (\frac{π}{12})}{sin (\frac{π}{3})} \approx 7.77$ $rArrA=(26sin(pi/12))/(sin(pi/3))~~ 7.77$

$\Rightarrow area( A) = \frac{1}{2} \times 7.77 \times 26 \times sin (\frac{7 π}{12})$ $rArr"area( A)"=1/2xx7.77xx26xxsin((7pi)/12)$

$\Rightarrow a r e a A \approx 97.568 to 3 dec. places$ $color(white)(rArrareaA)~~ 97.568" to 3 dec. places"$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{7 π}{12}$ $(7pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 26, 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 7π12(7pi)/12 and the angle between sides B and C is π12pi/12. If side B has a length of 26, 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 $\frac{7 π}{12}$ $(7pi)/12$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 26, what is the area of the triangle?