Jakotheshadows
New member
- Joined
- Jun 29, 2008
- Messages
- 47
Quote:
"While visiting the Sand Dunes National Park in Colorado, Cole approximated the angle of elevation to the top of a sand dune to be 20°. After walking 800 ft closer, he guessed that the angle of elevation had increased by 15°. Approximately how tall is the dune he was observing?"
If I could give you the picture I would, but I've tried everything I can think of to figure this out and the closest I came to my own solution was completely wrong.
I first noted that the angle between a hypothetical rod inserted into the highest point in the dune all the way to the dune's base and Cole's original position would have been 70° as the complement to the angle of elevation. I then assumed that the angle of elevation at 800 ft closer to the dune was 35°, and of course its complement is 55°. I tried approaching the problem by unsuccessfully figuring the original hypotenuse (or distance from Cole's original position to the top of the dune). Then I tried to figure out how much distance was left between Cole and the center of the dune (in order to make it a right triangle) and failed.
My next attack was to make a right triangle with the existing angle of elevation and using 800ft as one of the legs. With a 20/70/90 right triangle, I figured that the triangles other leg would be approx 291.2 ft and the hypotenuse would be approx 851.3 ft. My next train of thought brought me to the connection that when Cole got 800 ft closer, the angle of elevation increased by 15°. Assuming that the angle of elevation would increase by 15° for every 800 ft closer that Cole moved towards the dune, I mathematically came to the conclusion that from the center of the dune at ground level, Cole would have to dig a tunnel approximately 3,508.9(Cos 55°) ft straight up to get to the top of the dune.
Anyone care to shed some light upon my silly ignorance?
"While visiting the Sand Dunes National Park in Colorado, Cole approximated the angle of elevation to the top of a sand dune to be 20°. After walking 800 ft closer, he guessed that the angle of elevation had increased by 15°. Approximately how tall is the dune he was observing?"
If I could give you the picture I would, but I've tried everything I can think of to figure this out and the closest I came to my own solution was completely wrong.
I first noted that the angle between a hypothetical rod inserted into the highest point in the dune all the way to the dune's base and Cole's original position would have been 70° as the complement to the angle of elevation. I then assumed that the angle of elevation at 800 ft closer to the dune was 35°, and of course its complement is 55°. I tried approaching the problem by unsuccessfully figuring the original hypotenuse (or distance from Cole's original position to the top of the dune). Then I tried to figure out how much distance was left between Cole and the center of the dune (in order to make it a right triangle) and failed.
My next attack was to make a right triangle with the existing angle of elevation and using 800ft as one of the legs. With a 20/70/90 right triangle, I figured that the triangles other leg would be approx 291.2 ft and the hypotenuse would be approx 851.3 ft. My next train of thought brought me to the connection that when Cole got 800 ft closer, the angle of elevation increased by 15°. Assuming that the angle of elevation would increase by 15° for every 800 ft closer that Cole moved towards the dune, I mathematically came to the conclusion that from the center of the dune at ground level, Cole would have to dig a tunnel approximately 3,508.9(Cos 55°) ft straight up to get to the top of the dune.
Anyone care to shed some light upon my silly ignorance?