A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{12}$ $(pi)/12$ , the angle between sides B and C is $\frac{7 π}{12}$ $(7pi)/12$ , and the length of B is 17, what is the area of the triangle?

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Answer 1 · 2018-06-03T01:23:06

Area of triangle $A_{t} = 139.57$ $color(green)(A_t = 139.57$ sq units

$ˆ A = \frac{7 π}{12}, ˆ C = \frac{π}{12}, ˆ B = \frac{π}{3}, b = 17$ $hat A = (7pi)/12, hat C = pi/12, hat B = pi/3, b = 17$

Applying Law of Sines, $\frac{a}{sin A} = \frac{b}{sin B}$ $a / sin A = b / sin B$

$a = \frac{17 \cdot sin (\frac{7 π}{12})}{sin (\frac{π}{3})} = 18.96$ $a = (17 * sin ((7pi)/12) )/ sin (pi/3) = 18.96$

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

$A_{t} = (\frac{1}{2}) \cdot 18.96 \cdot 17 \cdot sin (\frac{π}{12}) = 139.57$ $A_t = (1/2) * 18.96 * 17 * sin (pi/12) = 139.57$ sq units

A triangle has sides A, B, and C. If the angle between sides A and B is π12(pi)/12, the angle between sides B and C is 7π12(7pi)/12, and the length of B is 17, what is the area of the triangle?