SOLUTION: With the sun, a six foot tall man casts a shadow that is 8 feet long. A nearby tree casts a shadow 92 feet long. Approximately how tall is the tree?

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Question 632432: With the sun, a six foot tall man casts a shadow that is 8 feet long. A nearby tree casts a shadow 92 feet long. Approximately how tall is the tree?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
All the rays of light from the sun are parallel and make the same angle to the ground.
The ground is horizontal.
The tree and the man are standing perfectly vertical.
Similar right triangles (same angles, proportional sides) are formed by each vertical item (man or tree), its horizontal shadow, and the slanted ray of sunlight that grazes the top of that vertical item and reaches the top of its shadow.
The drawing below (not drawn to scale) illustrates that.
Sun rays are red, tree is green, person is the short blue line next to the 6.
The ratio of vertical leg length to horizontal leg length is the same for those two similar right triangles, so the height h of the tree is such that
h%2F92=6%2F8 --> h=6%2A92%2F8=3%2A92%2F4=276%2F4=69
The tree is highlight%2869%29 feet tall.

NOTE:
I had already answered a very similar problem (problem 631101), and there are many similar questions answered. Searching for a similar problem is not easy (I could not figure out how to find them by searching), but if you look up one of them by number, a list of "related questions shows up on the right side of the screen.