To solve this problem, we will use the trigonometric function tangent.
Recall that by definition, in a right triangle:
[tex]tan\theta=\frac{opposite\text{ leg}}{adjacent\text{ leg}}.[/tex]
Therefore:
[tex]tan30^{\circ}=\frac{AB}{15}.[/tex]
Solving for AB, we get:
[tex]AB=tan30^{\circ}\times15.[/tex]
Finally, we get:
[tex]AB=5\sqrt{3}.[/tex]
Answer:
[tex]5\sqrt{3}.[/tex]
