A triangle has sides A, B, and C. The angle between sides A and B is pi/4 and the angle between sides B and C is pi/12. If side B has a length of 42, what is the area of the triangle?

1 Answer
sankarankalyanam
Dec 3, 2017

Area of Delta = 187.5281

Explanation:

/_ A = pi/12, /_ C = pi/4, /_ B = (pi - ((pi/12) + (pi/4))) = (2pi)/3

A / sin A = B / sin B = C / sin C

A / sin (pi/12) = 42/ sin ((2pi)/3) = C / sin (pi/4)

A = ( 42 * sin (pi/12)) / sin ((2pi)/3) = (42 * 9.2588)/0.866 = 12.5515

C = (42 * sin (pi/4)) / sin ((2pi)/3) = (42 * 0.707)/0.866 = 34.2887

Semi perimeter s = (A + B + C)/2 = (12.5515 + 42 + 34.2887)/2
s = 44.4201

s-A = 44.4201-12.5515 = 31.8686
s-B = 44.4201-42 = 2.4201
s-C = 44.4201-34.2887 = 10.1314

Area of Delta = sqrt(s (s-A) (s-B) (s-C))
Area of Delta = sqrt(44.4201 * 31.8686 * 2.4201 * 10.1314)
Area of Delta = sqrt(35166.8011) = 187.5281

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