A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{4}$ $pi/4$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 10, 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 $\frac{π}{4}$ $pi/4$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 10, what is the area of the triangle?

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Answer 1 · 2018-03-27T02:29:32

$A_{t} = (\frac{1}{2}) \cdot a \cdot b \cdot sin C = 10.6 sq units$ $color(brown)(A_t = (1/2) * a * b * sin C = 10.6 " sq units"$

Explanation:

$ˆ A = \frac{π}{12}, ˆ C = \frac{π}{4}, b = 10$ $hat A = pi/12, hat C = pi/4, b = 10$

$ˆ B = π - \frac{π}{12} - \frac{π}{4} = \frac{2 π}{3}$ $hat B = pi - pi/12 - pi/4 = (2pi)/3$

![http://www.dummies.com/education/math/trigonometry/laws-of-sines-and-cosines/](useruploads.socratic.org)

Applying the law of sines,

$a = \frac{b \cdot sin A}{sin B} = \frac{10 \cdot sin (\frac{π}{12})}{sin (\frac{2 π}{3})} \approx 3 units$ $a = (b * sin A ) / sin B = (10 * sin (pi/12)) / sin ((2pi)/3) ~~ 3 " units"$

$Area of the triangle A_{t} = (\frac{1}{2}) \cdot a \cdot b \cdot sin C$ $"Area of the triangle " A_t = (1/2) * a * b * sin C$

$A_{t} = (\frac{1}{2}) \cdot 3 \cdot 10 \cdot sin (\frac{π}{4}) = 10.6 sq units$ $color(brown)(A_t = (1/2) * 3 * 10 * sin (pi/4) = 10.6 " sq units"$

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{4}$ $pi/4$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 10, 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 pi/4π4pi/4 and the angle between sides B and C is pi/12π12pi/12. If side B has a length of 10, what is the area of the triangle?

1 Answer

Explanation:

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A triangle has sides A, B, and C. The angle between sides A and B is $\frac{π}{4}$ $pi/4$ and the angle between sides B and C is $\frac{π}{12}$ $pi/12$ . If side B has a length of 10, what is the area of the triangle?