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 $\frac{π}{4}$ $pi/4$ , and the length of B is 5, what is the area of the triangle?

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Answer 1 · 2018-06-03T10:12:05

Area $A_{t} = 7.92$ $A_t color(brown)(= 7.92$ sq units

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

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

$ˆ A = \frac{π}{4}, ˆ C = \frac{π}{3}, ˆ B = \frac{5 π}{12}, b = 5$ $hat A = pi/4, hat C = pi/3, hat B = (5pi)/12, b = 5$

$a = \frac{5 \cdot sin (\frac{π}{4})}{sin (\frac{5 π}{12})} = 3.66$ $a = (5 * sin (pi/4)) / sin ((5pi)/12) = 3.66$

$A_{t} = (\frac{1}{2}) \cdot 3.66 \cdot 5 \cdot sin (\frac{π}{3}) = 7.92$ $A_t= (1/2) * 3.66 * 5 * sin (pi/3) color(brown)(= 7.92$ sq units

A triangle has sides A,B, and C. If the angle between sides A and B is (pi)/3π3(pi)/3, the angle between sides B and C is pi/4π4pi/4, and the length of B is 5, what is the area of the triangle?