To determine the height of the apple tree, we'll use the concept of similar triangles. The apple tree and the wrong way sign form two triangles with their shadows, where the heights of the trees are proportional to the lengths of their shadows.
Here's how we can calculate the height of the apple tree:
1. We are given that the wrong way sign is 8 feet tall and casts a shadow that is 15 feet long.
2. We are also given that the shadow of the apple tree is 30 feet long.
Using the ratios of corresponding sides of similar triangles, we can set up the following proportion:
Height of Wrong Way Sign / Shadow of Wrong Way Sign = Height of Apple Tree / Shadow of Apple Tree
Substitute in the known values:
8 feet / 15 feet = Height of Apple Tree / 30 feet
Now, we solve for the Height of the Apple Tree:
Height of Apple Tree = (Height of Wrong Way Sign / Shadow of Wrong Way Sign) * Shadow of Apple Tree
Height of Apple Tree = (8 feet / 15 feet) * 30 feet
To find the apple tree's height, we simply cross-multiply and solve for our unknown:
Height of Apple Tree = 8 * 30 / 15
Height of Apple Tree = 240 / 15
Height of Apple Tree = 16 feet
So, the height of the apple tree is 16 feet.
