A triangle has sides A, B, and C. The angle between sides A and B is $pi/6$ and the angle between sides B and C is $pi/12$ . If side B has a length of 25, what is the area of the triangle?

Question

1522 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-03T11:42:49

$color(maroon)("Area of Triangle " A_t = 57.2 " sq units"$

$color(blue)("Given " hat A = pi/12, hat C = pi/6, hat B = pi - pi/12 - pi/6 = (3pi)/4, b = 25$

$"As per " color(red)("Law of Sines", color(green)(a / sin A = b / sin B = c / sin C$

$a / sin (pi/12) = 25 / sin ((3pi)/4) = c / sin (pi/6)$

$c = (25 * sin (pi/6)) / sin ((3pi)/4) = 17.68$

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

$A_t = (1/2) * 25 * 17.68 * sin (pi/12) = 57.2 " sq units"$

A triangle has sides A, B, and C. The angle between sides A and B is pi/6pi/6 and the angle between sides B and C is pi/12pi/12. If side B has a length of 25, what is the area of the triangle?