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 1, 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 1, what is the area of the triangle?

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Answer 1 · 2018-07-03T09:30:33

$Area of Triangle A_{t} = 1.183$ $color(magenta)("Area of Triangle " A_t = 1.183$

Explanation:

$ˆ A = \frac{π}{12}, ˆ C = \frac{π}{4}, ˆ B = \frac{2 π}{3}, b = 1$ $hat A = pi/12, hat C = pi/4, hat B = (2pi)/3, b = 1$

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As per Law of sines,

$a = \frac{b \cdot sin A}{sin B} = \frac{1 \cdot sin (\frac{2 π}{3})}{sin (\frac{π}{12})}$ $a = (b * sin A) / sin B = (1 * sin ((2pi)/3)) / sin (pi/12)$

$a = 3.346$ $a = 3.346$

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

$A_{t} = (\frac{1}{2}) \cdot 3.346 \cdot 1 \cdot sin (\frac{π}{4}) = 1.183$ $A_t = (1/2) * 3.346 * 1 * sin (pi/4) = 1.183$

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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 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. The angle between sides A and B is π4pi/4 and the angle between sides B and C is π12pi/12. If side B has a length of 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. 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 1, what is the area of the triangle?