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 $\frac{3 π}{4}$ $(3pi)/4$ , and the length of side B is 9, 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 $\frac{π}{12}$ $(pi)/12$ , the angle between sides B and C is $\frac{3 π}{4}$ $(3pi)/4$ , and the length of side B is 9, what is the area of the triangle?

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Answer 1 · 2016-06-27T09:21:03

Area of triangle is 14.777

Explanation:

Length of side b = 9

Angle between sides a and b = $\frac{π}{12}$ $pi/12$ = $∠ C$ $/_C$

Angle between sides b and c = $\frac{3 π}{4}$ $(3pi)/4$ = $∠ A$ $/_A$

Sum of the angles of a $△$ $triangle$ = $π$ $pi$

Hence, angle between c and a = $∠ B$ $/_B$ = $π - (\frac{π}{12} + \frac{9 π}{12})$ $pi - (pi/12 + (9pi)/12)$ = $(\frac{2 π}{12})$ $((2pi)/12)$ = $\frac{π}{6}$ $pi/6$

Using sine rule = $\frac{a}{sin A} = \frac{b}{sin B} = \frac{c}{sin C}$ $a/sin A = b/ sin B = c/ sin C$ ,

we get $\frac{b}{sin (\frac{π}{6})} = \frac{a}{sin (\frac{3 π}{4})} = \frac{c}{sin (\frac{π}{12})}$ $b/ sin (pi/6) =a/sin ((3pi)/4) = c/(sin (pi/12))$

$\frac{9}{\frac{1}{2}} = \frac{a}{sin (\frac{3 π}{4})} = \frac{c}{sin (\frac{π}{12})}$ $9/ (1/2) =a/sin ((3pi)/4) = c/(sin (pi/12))$

$a = 18 \cdot sin (\frac{3 π}{4})$ $a = 18* sin ((3pi)/4)$ = $18 \cdot \frac{\sqrt{2}}{2}$ $18*(sqrt 2) / 2$ = $18 \cdot 0.707106781$ $18 * 0.707106781$ = $12.7279$ $12.7279$

A = $\frac{1}{2} \cdot a \cdot b \cdot sin C$ $1/2*a*b*Sin C$ = $\frac{1}{2} \cdot 12.7279 \cdot 9 \cdot sin (\frac{π}{12})$ $1/2*12.7279*9*Sin (pi/12)$

= $\frac{1}{2} \cdot 12.7279 \cdot 9 \cdot 2.58$ $1/2*12.7279*9*2.58$ = 14.777

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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 $\frac{3 π}{4}$ $(3pi)/4$ , and the length of side B is 9, 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 π12(pi)/12, the angle between sides B and C is 3π4(3pi)/4, and the length of side B is 9, what is the area of the triangle?

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Explanation:

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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 $\frac{3 π}{4}$ $(3pi)/4$ , and the length of side B is 9, what is the area of the triangle?