Answer:
[tex]j=8[/tex]
Step-by-step explanation:
Special right triangles:
The sides of all 30-60-90 triangles are in the proportion [tex]x:x\sqrt{3}:2x[/tex], where [tex]2x[/tex] is the hypotenuse of the triangle and [tex]x[/tex] is the side directly opposite to the 30 degree angle.
Since the base of the triangle is directly opposite to the 30 degree angle, the hypotenuse, j, must be equal to [tex]4\cdot 2=\boxed{8}[/tex]
Basic trig:
[tex]\sin 30^{\circ}=\frac{4}{j},\\j=\frac{4}{\sin 30^{\circ}}=\boxed{8}[/tex]
