A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 15, respectively. The angle between A and C is $\frac{π}{8}$ $(pi)/8$ and the angle between B and C is $\frac{7 π}{12}$ $(7pi)/12$ . What is the area of the triangle?

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A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 15, respectively. The angle between A and C is $\frac{π}{8}$ $(pi)/8$ and the angle between B and C is $\frac{7 π}{12}$ $(7pi)/12$ . What is the area of the triangle?

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Answer 1 · 2018-03-26T07:07:34

$Area of the triangle A_{t} = (\frac{1}{2}) a \cdot b \cdot sin C = 71.4 sq units$ $color(brown)("Area of the triangle " A_t = (1/2) a * b * sin C = 71.4 " sq units"$

Explanation:

$a = 12, ˆ A = \frac{7 π}{12}, b = 15, ˆ B = \frac{π}{8}$ $a = 12, hat A = (7pi)/12, b = 15, hat B = pi/8$

To find the area of the triangle.

Third angle $ˆ C = π - \frac{7 π}{12} - \frac{π}{8} = \frac{7 π}{24}$ $hat C = pi - (7pi)/12 - pi / 8 = (7pi) / 24$

Now we know, side a, side b and included ange C.

$A_{t} = (\frac{1}{2}) a \cdot b \cdot sin C = (\frac{1}{2}) \cdot 12 \cdot 15 \cdot sin (\frac{7 π}{24}) = 71.4 sq units$ $A_t = (1/2) a * b * sin C = (1/2) * 12 * 15 * sin ((7pi) / 24) = 71.4 " sq units"$

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A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 15, respectively. The angle between A and C is $\frac{π}{8}$ $(pi)/8$ and the angle between B and C is $\frac{7 π}{12}$ $(7pi)/12$ . What is the area of the triangle?

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A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 15, respectively. The angle between A and C is π8(pi)/8 and the angle between B and C is 7π12 (7pi)/12. What is the area of the triangle?

1 Answer

Explanation:

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A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 15, respectively. The angle between A and C is $\frac{π}{8}$ $(pi)/8$ and the angle between B and C is $\frac{7 π}{12}$ $(7pi)/12$ . What is the area of the triangle?