A 6-foot spruce tree is planted 15 feet from a lighted streetlight whose lamp is 18 feet above the ground. How many feet long is the shadow of that tree?
6/x = 18/(15+x)
6(15+x) = 18x
90+6x = 18x
12x = 90
x = 7.5
Does this help? :-)
The answer would be 7.5 :-)
yes! thank you! I have another but I don't know how to put the picture into one of these boxes :)It's suppose to be a big triangle... In the figure below, the lengths of DE, EF, and FG are given, in units. What is the area, in square units, of triangle DEG?
G
/ /|
/ / |
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/ / |10
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/______/_____|
D 12 7 F
To find the length of the shadow of the tree, we can use similar triangles. Let's call the length of the shadow "x".
Step 1: Understand the problem.
- We have a spruce tree that is 6 feet tall.
- The tree is planted 15 feet away from a lighted streetlight.
- The lamp of the streetlight is 18 feet above the ground.
- We want to find the length of the shadow of the tree (x).
Step 2: Draw a diagram.
- Draw a vertical line to represent the tree (6 feet tall).
- Draw a horizontal line from the top of the tree to represent the shadow of the tree.
- Draw a vertical line from the top of the tree to represent the streetlight (18 feet tall).
- Label the distance between the tree and the streetlight as 15 feet.
Step 3: Identify similar triangles.
- We have two triangles that are similar: the tree-shadow triangle and the tree-streetlight triangle.
Step 4: Set up a proportion.
- Since the triangles are similar, we can set up a proportion to find the length of the shadow.
- The height of the tree corresponds to the height of the streetlight in the same way that the length of the shadow corresponds to the distance between the tree and the streetlight.
- The proportion is: (length of shadow)/(distance between tree and streetlight) = (height of tree)/(height of streetlight).
- Plugging in the values, we have: x/15 = 6/18.
Step 5: Solve the proportion.
- Cross-multiply: 18x = 15 * 6.
- Simplify: 18x = 90.
- Divide both sides by 18: x = 90/18.
- Compute: x = 5.
Therefore, the length of the shadow of the tree is 5 feet.