A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 8, respectively. The angle between A and C is $\frac{π}{12}$ $(pi)/12$ and the angle between B and C is $\frac{5 π}{6}$ $(5pi)/6$ . 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 5 and 8, respectively. The angle between A and C is $\frac{π}{12}$ $(pi)/12$ and the angle between B and C is $\frac{5 π}{6}$ $(5pi)/6$ . What is the area of the triangle?

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Answer 1 · 2018-03-27T02:52:55

$A_{t} = (\frac{1}{2}) a b sin C = (\frac{1}{2}) \cdot 5 \cdot 8 \cdot sin (\frac{π}{12}) = 5.18 sq units$ $color(red)(A_t = (1/2) a b sin C = (1/2) * 5 * 8 * sin (pi/12) = 5.18 " sq units"$

Explanation:

$a = 5, b = 8, ˆ A = \frac{5 π}{6}, ˆ B = \frac{π}{12}$ $a = 5, b = 8, hat A = (5pi)/6, hat B = pi/12$

To find the area of the triangle.

$ˆ C = π - \frac{5 π}{6} - \frac{π}{12} = \frac{π}{12}$ $hat C = pi - (5pi)/6 - pi/12 = pi/12$

It's an isosceles triangle with $ˆ B = ˆ C & hence b = c = 8$ $hat B = hat C " & hence " b = c = 8$

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Formula for Area of triangle, knowing 2 sides and included angle

$A_{t} = (\frac{1}{2}) a b sin C = (\frac{1}{2}) \cdot 5 \cdot 8 \cdot sin (\frac{π}{12}) = 5.18 sq units$ $color(red)(A_t = (1/2) a b sin C = (1/2) * 5 * 8 * sin (pi/12) = 5.18 " sq units"$

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A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 8, respectively. The angle between A and C is $\frac{π}{12}$ $(pi)/12$ and the angle between B and C is $\frac{5 π}{6}$ $(5pi)/6$ . What is the area of the triangle?

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Explanation:

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A triangle has sides A, B, and C. Sides A and B have lengths of 5 and 8, respectively. The angle between A and C is π12(pi)/12 and the angle between B and C is 5π6 (5pi)/6. 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 5 and 8, respectively. The angle between A and C is $\frac{π}{12}$ $(pi)/12$ and the angle between B and C is $\frac{5 π}{6}$ $(5pi)/6$ . What is the area of the triangle?