The given information is:
- The steep angle of elevation is 32.8
- The vertical rise is 800 ft.
A diagram of the situation is:
If we look at the diagram, we can see a triangle, and we need to know the hypotenuse. As we know the angle and the opposite side, we can use the trigonometric function sine, which is given by the following formula:
[tex]\sin \theta=\frac{opposite}{hypotenuse}[/tex]If we replace the know values, we can solve for hypotenuse as follows:
[tex]\begin{gathered} \sin 32.8\degree=\frac{880ft}{x} \\ x=\frac{880ft}{\sin 32.8\degree} \\ x=\frac{880ft}{0.54} \\ x=1624.5\text{ ft} \end{gathered}[/tex]Then, you traveled 1624.5 ft when you finally reach the top of the mountain.
