A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $pi/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 2, 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 $\frac{π}{6}$ $pi/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 2, what is the area of the triangle?

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Answer 1 · 2018-02-17T04:02:02

$A_{t} = (\frac{1}{2}) a b sin C = 0.3661$ $A_t = (1/2) a b sin C =color(green)( 0.3661$

Explanation:

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$C = \frac{π}{6}, A = \frac{π}{12}, b = 2$ $C = pi/6, A = pi/12, b = 2$

$ˆ B = π - \frac{π}{12} - \frac{π}{6} = \frac{3 π}{4}$ $hatB = pi - pi/12 - pi/6 = (3pi)/4$

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

$a = \frac{b \cdot sin A}{sin B} = \frac{2 \cdot sin (\frac{π}{12})}{sin (\frac{3 π}{4})} = 0.7321$ $a = (b * sin A) / sin B = (2 * sin (pi/12)) / sin ((3pi)/4) = 0.7321$

$A_{t} = (\frac{1}{2}) a b sin C = (\frac{1}{2}) \cdot 0.7321 \cdot 2 \cdot sin (\frac{π}{6}) = 0.3661$ $A_t = (1/2) a b sin C = (1/2) * 0.7321* 2 * sin (pi/6) = 0.3661$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{6}$ $pi/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 2, 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 π6pi/6 and the angle between sides B and C is π12pi/12. If side B has a length of 2, 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 $\frac{π}{6}$ $pi/6$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 2, what is the area of the triangle?