A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 7, respectively. The angle between A and C is $\frac{17 π}{24}$ $(17pi)/24$ and the angle between B and C is $\frac{5 π}{24}$ $(5pi)/24$ . What is the area of the triangle?

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Answer 1 · 2018-03-27T02:34:58

$A_{t} = (\frac{1}{2}) \cdot a \cdot b \cdot sin C = 7.25 sq units$ $color(blue)(A_t = (1/2) * a * b * sin C = 7.25 " sq units"$

$a = 8, b = 7, ˆ A = \frac{5 π}{24}, ˆ B = \frac{17 π}{24}$ $a = 8, b = 7, hat A = (5pi)/24, hat B = (17pi)/24$

$Sum of the three angles of a triangle = π^{c}$ $"Sum of the three angles of a triangle " = pi^c$

$ˆ C = π - ˆ A - ˆ B = π - \frac{5 π}{24} - \frac{17 π}{24} = \frac{π}{12}$ $hat C = pi - hat A - hat B = pi - (5pi)/24 - (17pi)/24 = pi/12$

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

$A_{t} = (\frac{1}{2}) \cdot 8 \cdot 7 \cdot sin (\frac{π}{12}) = 7.25 sq units$ $color(blue)(A_t = (1/2) * 8 * 7 * sin (pi/12) = 7.25 " sq units"$

A triangle has sides A, B, and C. Sides A and B have lengths of 8 and 7, respectively. The angle between A and C is 17π24(17pi)/24 and the angle between B and C is 5π24 (5pi)/24. What is the area of the triangle?