SOLUTION: Solve the problem. By holding a ruler 3 feet in front of her eyes as illustrated in the diagram, Carla sees that the top and bottom points of a vertical cliff face line up with

Algebra ->  Length-and-distance -> SOLUTION: Solve the problem. By holding a ruler 3 feet in front of her eyes as illustrated in the diagram, Carla sees that the top and bottom points of a vertical cliff face line up with       Log On


   

Question 206710: Solve the problem.
By holding a ruler 3 feet in front of her eyes as illustrated in the diagram, Carla sees that the top and bottom points of a vertical cliff face line up with marks separated by 4" on the ruler. According to the map, Carla is about a half mile from the cliff. What is the approximate height of the cliff rounded to the nearest foot? Recall that a mile is 5280 feet.

(I dont know if this problem is solvable without the pictue, but it is basically Carla viewing the mountain from a particulat distance)
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Use the properties of similar triangles. The triangle formed by her arm, the ruler and the hypotenuse AND the triangle formed by 1/2 mile, the cliff and that hypotenuse are similar.
So
armLength%2FhalfMile+=+4inch%2FcliffHeight
convert everything to feet
halfMile = 5280/2 = 2640
4inches = 1/3 foot
3%2F2640+=+%281%2F3%29%2FCliff
Cliff+=+%281%2F3%29%2A2640%2F3
Cliff+=+293+feet
Note that this is a very rough estimate. No way Carla has a three foot arm. No way even the littlest error in the 4inches doesnt translate to a huge error on the size of the cliff. But, is better than a wild guess