Idon't understand how to work this out, can someone me? ?

To solve this, we need to use the law of sines...SinA/a = SinB/b = SinC/c

if we think of this as a triangle...the other side of the 55 degrees is our ∠A (35°)...find this by 90 - 55 = 35. Let side a = X. Side c = 4 and ∠C = 90°

now let's do some math...

sin90 / 4  =  sin35 / x      (multiply both sides by x)
xsin90 / 4 = sin35            (multiply both sides by 4)
xsin90 = 4sin35              (divide both sides by sin90)
x = 4sin35 / sin90
x = 2.29