A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{3}$ $pi/3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 8, 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 $\frac{π}{3}$ $pi/3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 8, what is the area of the triangle?

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Answer 1 · 2018-02-17T10:29:20

$A_{t} = (\frac{1}{2}) a b sin C = 7.4256$ $A_t = (1/2) a b sin C =color(green)( 7.4256$

Explanation:

$ˆ A = \frac{π}{12}, ˆ C = \frac{π}{3}, b = 8$ $hatA = pi/12, hatC = pi/3, b = 8$

$ˆ B = π - \frac{π}{12} - \frac{π}{3} = \frac{7 π}{12}$ $hatB = pi - pi/12 - pi/3 = (7pi)/12$

$\frac{a}{sin A} = \frac{b}{sin B}$ $a / sin A = b / sin B$

$a = \frac{8 \cdot sin (\frac{π}{12})}{sin (\frac{7 π}{12})} = 2.1436$ $a = (8 * sin(pi/12))/sin ((7pi)/12) = 2.1436$

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$A_{t} = (\frac{1}{2}) a b sin C = (\frac{1}{2}) \cdot 2.1436 \cdot 8 sin (\frac{π}{3}) = 7.4256$ $A_t = (1/2) a b sin C = (1/2) * 2.1436 * 8 sin (pi/3) =color(green)( 7.4256$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{3}$ $pi/3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 8, what is the area of the triangle?

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Explanation:

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A triangle has sides A, B, and C. The angle between sides A and B is π3pi/3 and the angle between sides B and C is π12pi/12. If side B has a length of 8, 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 $\frac{π}{3}$ $pi/3$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 8, what is the area of the triangle?