Question 256498: The problem is: An ant is 120 ft. from an 80ft. tall tree whose top is the visual line of a 600 ft. tall bldg. How far is tree from building? The teacher gave this: 280/3120 = 600/120 + x. Then he cross multiplied and got
240 + 2x = 1800 then he solved for x and got x = 780 ft. as answer. I have no idea where the 280 or 3120 came from...can anyone help? Thank you. This is for 9th grade Algebra I.
Found 2 solutions by ptaylor, Greenfinch:
Answer by ptaylor(2198)   (Show Source):
You can put this solution on YOUR website!
I don't know where he got those numbers, either but here's how I work the problem: Imagine the ant looking up and seeing the top of an 80' tree and in the distance (x feet from the tree), he sees the top of a 600' building. Now you basically have two right triangles, the smaller one contained inside the larger one. The opposite side of the smaller triangle is the 80' tree and the adjacant side is the 120' distance to the tree. The opposite side of the larger triangle is the 600' building and the adjacant side is the 120' PLUS x, the distance from the tree to the building. Now let's set up a ratio:
OPP/ADJ of smaller triangle = OPP/ADJ of larger triangle ; or
80/120=600/(120+x) now we cross multiply
9600+80x=72000
80x=62,400
x=780'
Hope this helps----ptaylor
Answer by Greenfinch(383)  (Show Source):
You can put this solution on YOUR website! Think of this in terms of similar triangles. Tree is 80 ft high, building is 600 ft high, so ratio of 1 to 7 1/2. Distances are in the same ratio. Ant to tree is 120 so ant to building is 7 1/2 times 120. So ant to building is 900 feet. What they want is tree to building, which is ant to building less the 120 feet from ant to tree, so tree to building is 780 feet
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