A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 7, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{5 π}{8}$ $(5pi)/8$ . 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 7, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{5 π}{8}$ $(5pi)/8$ . What is the area of the triangle?

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Answer 1 · 2018-03-26T07:01:41

$Area of the triangle A_{t} \approx 10.87 sq units$ $color(indigo)("Area of the triangle "A_t ~~ 10.87 " sq units"$

Explanation:

$a = 12, b = 7, ˆ A = \frac{5 π}{8}, ˆ B = \frac{7 π}{24}$ $a = 12, b = 7, hatA = (5pi)/8, hat B = (7pi)/24$

$ˆ C = π - ˆ A - ˆ B = π - \frac{5 π}{8} - \frac{7 π}{24} = \frac{π}{12}$ $hat C = pi - hat A - hat B = pi - (5pi)/8 - (7pi)/24 = pi/12$

Having known, two sides and the included angle (SAS), area of the triangle is given by the formula

$A_{t} = (\frac{1}{2}) a b sin C = (\frac{1}{2}) \cdot 12 \cdot 7 \cdot sin (\frac{π}{12}) \approx 10.87 sq units$ $color(indigo)(A_t = (1/2) a b sin C = (1/2) * 12 * 7 * sin (pi/12) ~~ 10.87 " sq units"$

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A triangle has sides A, B, and C. Sides A and B have lengths of 12 and 7, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{5 π}{8}$ $(5pi)/8$ . 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 7, respectively. The angle between A and C is 7π24(7pi)/24 and the angle between B and C is 5π8 (5pi)/8. 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 7, respectively. The angle between A and C is $\frac{7 π}{24}$ $(7pi)/24$ and the angle between B and C is $\frac{5 π}{8}$ $(5pi)/8$ . What is the area of the triangle?