A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{3}$ $pi/3$ , the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , and the length of B is 1, what is the area of the triangle?

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{3}$ $pi/3$ , the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , and the length of B is 1, what is the area of the triangle?

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Answer 1 · 2018-05-19T16:38:44

$A_{t} = 0.4019$ $color(blue)(A_t = 0.4019$ sq units

Explanation:

$ˆ A = \frac{π}{12}, ˆ C = \frac{π}{3}, ˆ B = π - \frac{π}{12} - \frac{π}{3} = \frac{7 π}{12}, b = 1$ $hat A = (pi)/12, hat C = pi/3, hat B = pi - pi/12 - pi/3 = (7pi)/12, b = 1$

Applying Law of Sines,

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

$a = \frac{1 \cdot sin (\frac{π}{12})}{sin (\frac{7 π}{12})}$ $a = (1 * sin (pi/12))/sin ((7pi)/12)$

$a = 0.2679$ $a = 0.2679$

Area of Triangle $A_{t} = (\frac{1}{2}) a b sin C$ $A_t = (1/2) a b sin C$

$A_{t} = (\frac{1}{2}) \cdot 0.2679 \cdot 1 \cdot sin (\frac{π}{3})$ $A_t = (1/2) * 0.2679 * 1 * sin (pi/3)$

$A_{t} = 0.4019$ $color(blue)(A_t = 0.4019$ sq units

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{3}$ $pi/3$ , the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , and the length of B is 1, what is the area of the triangle?

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Explanation:

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{3}$ $pi/3$ , the angle between sides B and C is $\frac{π}{12}$ $pi/12$ , and the length of B is 1, what is the area of the triangle?