A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 7, respectively. The angle between A and C is $\frac{π}{4}$ $(pi)/4$ and the angle between B and C is $\frac{π}{8}$ $(pi)/8$ . What is the area of the triangle?

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Answer 1 · 2018-02-17T09:56:31

Doesn’t qualify to form a triangle

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

Given $a = 4, b = 7, ˆ B = \frac{π}{4}, ˆ A = \frac{π}{8}$ $a = 4, b = 7, hatB = pi/4, hatA = pi/8$

$ˆ C = π - \frac{π}{8} - \frac{π}{4} = \frac{5 π}{8}$ $hat C = pi - pi/8 - pi/4 = (5pi)/8$

$\frac{a}{sin A} = \frac{4}{sin (\frac{π}{8})} = 10.4525$ $a / sin A = 4 / sin (pi/8) = 10.4525$

$\frac{b}{sin B} = \frac{7}{sin (\frac{π}{4})} = 9.8995$ $b / sin B = 7 / sin (pi/4) = 9.8995$

$\frac{a}{sin A} \neq \frac{b}{sin B}$ $a / sin A != b / sin B$

Hence doesn’t qualify to form a triangle

A triangle has sides A, B, and C. Sides A and B have lengths of 4 and 7, respectively. The angle between A and C is π4(pi)/4 and the angle between B and C is π8 (pi)/8. What is the area of the triangle?