The given figure can be redrawn as,
The length of base, b=1000 ft.
In the triangle, BC is,
[tex]BC=\frac{BD}{2}=\frac{b}{2}=\frac{1000}{2}=500\text{ ft}[/tex]
Applying trigonometric property in triangle ABC,
[tex]\begin{gathered} \cos 57^{\circ}=\frac{adjacent\text{ side}}{hypotenuse} \\ \cos 57^{\circ}=\frac{BC}{AB} \\ \cos 57^{\circ}=\frac{500}{AB} \\ AB=\frac{500}{\cos 57^{\circ}} \end{gathered}[/tex]
Hence,
[tex]AB=918\text{ ft}[/tex]
Therefore, the sliding slope of the mountain is 918 ft.
