A triangle has sides A, B, and C. If the angle between sides A and B is $\frac{π}{6}$ $(pi)/6$ , the angle between sides B and C is $\frac{2 π}{3}$ $(2pi)/3$ , and the length of side B is 25, what is the area of the triangle?

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Answer 1 · 2018-04-10T03:01:02

$:.color(green)(A_t = (1/2) * 25 * 25 * sin ((2pi)/3) = 270.63 " sq units"$

$hat A = (2pi)/3, hat C = pi/6, hat B = pi - pi/6 - (2pi)/3 = pi/3, b = 25$

It's an isosceles triangle with sides b & c equal.

$:. c = b = 25$

$color(blue)("Area of " Delta " " A_t = (1/2) * b * c * sin A$

$:.color(green)(A_t = (1/2) * 25 * 25 * sin ((2pi)/3) = 270.63 " sq units"$

A triangle has sides A, B, and C. If the angle between sides A and B is (pi)/6π6(pi)/6, the angle between sides B and C is (2pi)/32π3(2pi)/3, and the length of side B is 25, what is the area of the triangle?