# A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/3, the angle between sides B and C is (5pi)/12, and the length of B is 2, what is the area of the triangle?

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Feb 17, 2018

Area of triangle A_t = (1/2) * a * b * sin C = color(red)(2.5758

#### Explanation:

$\hat{C} = \frac{\pi}{3} , \hat{A} = \frac{5 \pi}{12} , b = 2$

$\hat{B} = \pi - \frac{5 \pi}{12} - \left(\frac{\pi}{3}\right) = \frac{\pi}{4}$

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

$a = \frac{2 \cdot \sin \left(\frac{5 \pi}{12}\right)}{\sin} \left(\frac{\pi}{4}\right) = 2.2307$

Area of triangle ${A}_{t} = \left(\frac{1}{2}\right) \cdot a \cdot b \cdot \sin C$

A_t = (1/2) * 2.2307 * 2 sin (pi/3) = color(red)(2.5758

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