Answer:
[tex]AB\approx 24.22[/tex]
Step-by-step explanation:
In any right triangle, the sine of an angle is equal to its opposite side divided by the hypotenuse of the triangle.
In this case, in order to form the ratio, we're looking for the angle to the bottom right of the triangle. Notice how this angle is the supplement to the angle marked [tex]130.8^{\circ}[/tex]. Since the two angles form one side of the line, we can solve for this angle.
Let's call the angle [tex]\theta[/tex]:
[tex]130.8+\theta=180,\\\theta=49.2^{\circ}[/tex]
From basic. trig for right triangles (refer to first paragraph in answer):
[tex]\sin 49.2^{\circ}=\frac{AB}{32},\\AB=32\sin 49.2^{\circ}=24.2238417809\approx \boxed{24.22}[/tex]
