we can make a triangle
we need to find x
we can use the trigonometric ratio of sine
[tex]\begin{gathered} \sin (\alpha)=\frac{O}{H} \\ \end{gathered}[/tex]
where alpha is the angle, O the opposite side from the angle and H the hypotenuse
so placing
[tex]\begin{gathered} \sin (12)=\frac{x}{15} \\ \\ x=15\sin (12) \\ x=3.12 \end{gathered}[/tex]
she climbs 3.12 miles vertically
