Question

What is the sliding slope of the mountain if the angle of elevation is 57o and the base is 1000 ft long? Round your answer to a nearest foot.

Answer 1

The given figure can be redrawn as,

The length of base, b=1000 ft.

In the triangle, BC is,

`BC=(BD)/(2)=(b)/(2)=(1000)/(2)=500\text{ ft}`

Applying trigonometric property in triangle ABC,

`\begin{gathered} \cos 57^(\circ)=\frac{adjacent\text{ side}}{hypotenuse} \\ \cos 57^(\circ)=(BC)/(AB) \\ \cos 57^(\circ)=(500)/(AB) \\ AB=(500)/(\cos 57^(\circ)) \end{gathered}`

Hence,

`AB=918\text{ ft}`

Therefore, the sliding slope of the mountain is 918 ft.