A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{4}$ $(pi)/4$ , the angle between sides B and C is $\frac{π}{6}$ $pi/6$ , and the length of B is 1, 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 $\frac{π}{4}$ $(pi)/4$ , the angle between sides B and C is $\frac{π}{6}$ $pi/6$ , and the length of B is 1, what is the area of the triangle?

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Answer 1 · 2018-08-10T07:49:04

$A_{t} = \frac{1}{2} a b sin C \approx 0.183, sq. units$ $color(indigo)(A_t = 1/2 a b sin C ~~ 0.183, " sq. units"$

Explanation:

$ˆ A = \frac{π}{6}, ˆ C = \frac{π}{4}, ˆ B = \frac{7 π}{12}, b = 1$ $hat A = pi/6, hat C = pi/4, hat B = (7pi)/12, b = 1$

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

$a = \frac{b \cdot sin A}{sin B} = \frac{1 \cdot sin (\frac{π}{6})}{sin (\frac{7 π}{12})}$ $a = (b * sin A) / sin B = (1 * sin (pi/6)) / sin ((7pi)/12)$

$a \approx 0.5176$ $a ~~ 0.5176$

$"Area of D" Delta = A_t = 1/2 a b sin C$

$color(indigo)(A_t = 1/2 * 0.5176 * 1 * sin (pi/4) ~~ 0.183, " sq. units"$

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A triangle has sides A,B, and C. If the angle between sides A and B is $\frac{π}{4}$ $(pi)/4$ , the angle between sides B and C is $\frac{π}{6}$ $pi/6$ , and the length of B is 1, 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 (pi)/4π4(pi)/4, the angle between sides B and C is pi/6π6pi/6, and the length of B is 1, 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 $\frac{π}{4}$ $(pi)/4$ , the angle between sides B and C is $\frac{π}{6}$ $pi/6$ , and the length of B is 1, what is the area of the triangle?