math trigonometry world problem

Question

Two angles of a triangle are 115° and 45°. The longest side is 8m longer than the shortest side. Determine the length of the longest side.

Answer 1

The smallest angle is 20, the smallest side is x, and the longest side is x+8

Law of sines:

sin 20/ x = sin 115/(x+8)

sin 115 * x = (sin 20)(x+8)

sin 115 * x = sin 20 * x + 8 * sin 20

sin 115 x - sin 20 x = 8 sin 20

x( sin 115 - sin 20) = 8 sin 20

x = (8 sin 20)/ ( sin 115 - sin 20)

x=4.8488765917524967316502527512429 is the shortest side

the longest side is 12.8488765917524967316502527512429