Answer to Question #6810 in Trigonometry for Dylan
If triangle ABC has an area of 3.75cm and a = 5cm and c = 3cm, find the length of b if angle B is obtuse?
S = 1/4*sqrt( (a+b+c)*(b+c-a)*(a+c-b)*(a+b-c) )
1/4*sqrt( (5+b+3)*(b+3-5)*(5+3-b)*(5+b-3) ) = 3.75
sqrt( (8+b)*(b-2)*(8-b)*(2+b) ) = 3.75*4
(8+b)*(b-2)*(8-b)*(2+b) = (15)²
-b^4+68b²-256 = 225
b^4 - 68b² + 481 = 0
We've got a quadratic equation. It's positive solutions are b1 = 8 and b2 = 2. As angle B is obtuse (angle B lies opposite b) we choose b = 8.