Question

You are going off roading in a 4x4 Jeep Wrangler in Colorado.You quickly drive up the side of a small mountian at a steep angle of elevation of 32.8Your vertical rise is 800ftHow far did you travel when you finally reach the top of the mountainRound to the nearest tenth

Answer 1

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:

`\sin \theta=(opposite)/(hypotenuse)`

If we replace the know values, we can solve for hypotenuse as follows:

`\begin{gathered} \sin 32.8\degree=(880ft)/(x) \\ x=(880ft)/(\sin 32.8\degree) \\ x=(880ft)/(0.54) \\ x=1624.5\text{ ft} \end{gathered}`

Then, you traveled 1624.5 ft when you finally reach the top of the mountain.