A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{8}$ $(pi)/8$ , the angle between sides B and C is $\frac{5 π}{6}$ $(5pi)/6$ , and the length of side B is 19, what is the area of the triangle?

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A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{8}$ $(pi)/8$ , the angle between sides B and C is $\frac{5 π}{6}$ $(5pi)/6$ , and the length of side B is 19, what is the area of the triangle?

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Answer 1 · 2018-02-17T08:19:00

Area of triangle $A_{t} = (\frac{1}{2}) a b sin C \approx ~ 264.5996$ $A_t = (1/2) a b sin C ~~ ~color(brown)( 264.5996$ sq units

Explanation:

Given $ˆ C = \frac{π}{8}, ˆ A = \frac{5 π}{6}, b = 19$ $hatC = pi/8, hatA = (5pi)/6, b = 19$

Third angle $ˆ B = π - (\frac{5 π}{6} + \frac{π}{8}) = \frac{π}{24}$ $hatB = pi - ((5pi)/6 + pi/8) = pi/24$

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

$a = \frac{19 \cdot sin (\frac{5 π}{6})}{sin (\frac{π}{24})} \approx 72.7823$ $a = (19 * sin ((5pi)/6)) / sin (pi/24)~~color(blue)( 72.7823$

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

$\Rightarrow (\frac{1}{2}) \cdot 19 \cdot 72.7823 \cdot sin ((\frac{π}{8}) \approx 264.5996$ $=> (1/2) * 19 * 72.7823 * sin((pi/8) ~~color(brown)( 264.5996$

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A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{8}$ $(pi)/8$ , the angle between sides B and C is $\frac{5 π}{6}$ $(5pi)/6$ , and the length of side B is 19, what is the area of the triangle?

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A triangle has sides A, B, and C. If the angle between sides A and B is π8(pi)/8, the angle between sides B and C is 5π6(5pi)/6, and the length of side B is 19, what is the area of the triangle?

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A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{8}$ $(pi)/8$ , the angle between sides B and C is $\frac{5 π}{6}$ $(5pi)/6$ , and the length of side B is 19, what is the area of the triangle?