# Answer to Question #6810 in Trigonometry for Dylan

Question #6810

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?

Expert's answer

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.

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.

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