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If Judy lies on the ground 45 feet from her tent Both the top of the tent and the top of a tall cliff are in her line of sight her tent is 10 feet tall about how high is the cliff?
Wiki User
∙ 12y ago
Without extra info this is unanswerable.....
But if you have the distance to the cliff with the other info you gave it can be solved. If you mean to say that the top of the cliff and the top of the tent appear to line up to an observer on the ground 45 feet away from the tent then the cliffs height will be proportionate to it's distance from the observer. To solve this using absolutely no math follow these steps, the math way is below...
Draw a horizontal line on graph paper and number it from 0 to how ever far it is to the cliff, put the numbers where the line is intersected by the vertical lines of the graph paper.
Place a point at 0 to represent Judy marked x. Place a point 10 graph paper squares up from 45 on the line you drew, this point is the top of the tent, mark this point y.
Use a ruler to draw a straight line from x to y, draw the line out until it crosses the line coming up from the number that is the same as how many feet it is to the cliff, mark the point where these lines cross z, this point is the cliff top. Count how many squares up it is from the line you drew to z. This is how many feet tall the cliff is.
There is an equation for this too. But it would also require the distance to the cliff. If you know the slope and the horizontal distance you can figure out height. If the line goes up one foot for every 4.5 feet traveled horizontally as in this case (10 foot tent height simplified to 1, 45 foot distance to tent simplified to 4.5 by dividing each by their greatest common denominator) the height of the cliff is the distance to it divided by 4.5. Thus if the cliff is 450 feet away it would have to be 100 feet high (450/4.5)
The pythagorean theorem mentioned by a poster earlier (I edited that out) would not work. You could use it to find the distance from the observer to the top of the tent since you have the distance and height of the tent, but this would not help you determine the distance from the observer to the cliff top, which along with the horizontal distance to the cliff bottom could give you the cliff height.
What you need is the slope of not the length of, the imaginary line between observer and tent top to extrapolate the height of that line as it goes out to infinity. With the slope you can figure out the height of the observer's sight line above any point along the horizontal base line.
Wiki User
∙ 12y ago
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