consider a triangle where B88 degrees a 55 and c21 Determine

consider a triangle where B=88 degrees, a =5.5 and c=2.1. Determine the area

applying law of cosines to find the 3rd side

b^2 = a^2 + c^2 - 2ac cos B

plugging the values

b^2 = 5.5^2 + 2.1^2 - 2(5.5)(2.1) cos 88

b = 5.82

now applying herons formula to find the area

s = ( 5.5 + 2.1 + 5.82)/2

area = sqrt ( s(s-a)(s-b)(s-c)

area = sqrt ( 6.71 ( 6.71 - 5.5) (6.71-2.1)(6.71-5.82)

area = 5.77