A triangle has two sides of lengths 8 and 6 cm. Find the length of the third side if its area is 24 cm^2.

The area A of the triangle is given by
:

(1/2)ab sinC = 24, where a and b are the sides and C is the angle
between the sides.

a = 8 and b = 6 and area =
24.

Therefore (1/2)8*6sinC = 24.

sinC =
24*2/(8*6) = 1/2.

Therefore C = 30 degree, or 150
deg.

If C = 30,  c ^2 = (a^2+b^2-
2abcosC)

 c = sqrt(8^2+6^2 - 2*8*6 cos30) = 4.1063
cm. nearly.

If C= 150 degree, then

c =
sqrt(8^2+6^2- 2*8*6*cos150) =  13.5329cm nearly.