A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{3}$ $(pi)/3$ , the angle between sides B and C is $\frac{5 π}{12}$ $(5pi)/12$ , and the length of B is 2, what is the area of the triangle?

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Answer 1 · 2018-02-17T03:38:59

Area of triangle $A_{t} = (\frac{1}{2}) \cdot a \cdot b \cdot sin C = 2.5758$ $A_t = (1/2) * a * b * sin C = color(red)(2.5758$

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$ˆ C = \frac{π}{3}, ˆ A = \frac{5 π}{12}, b = 2$ $hatC = pi/3, hat A = (5pi)/12, b = 2$

$ˆ B = π - \frac{5 π}{12} - (\frac{π}{3}) = \frac{π}{4}$ $hatB = pi - (5pi)/12 - (pi/3) = pi/4$

$\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a / sin A = b / sin B = c / sin C$

$a = \frac{2 \cdot sin (\frac{5 π}{12})}{sin (\frac{π}{4})} = 2.2307$ $a = (2 * sin ((5pi)/12)) / sin (pi/4) = 2.2307$

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

$A_{t} = (\frac{1}{2}) \cdot 2.2307 \cdot 2 sin (\frac{π}{3}) = 2.5758$ $A_t = (1/2) * 2.2307 * 2 sin (pi/3) = color(red)(2.5758$

A triangle has sides A, B, and C. If the angle between sides A and B is π3(pi)/3, the angle between sides B and C is 5π12(5pi)/12, and the length of B is 2, what is the area of the triangle?