A student notices that the shadows of a sign and a tree lie along the same line and end at the same point. The height of the sign is 3 feet. The length of the tree's shadow is 20 feet. The distance from the base of the sign to the vase of the tree is 16 feet. How tall is the tree?
20 - 16 = 4 ft. >> length of sign's shadow
Cross multiply and solve this proportion.
3/4 = x/20
15 ft
To find the height of the tree, we can set up a proportion using similar triangles. Let's call the height of the tree "h". We have the following information:
Height of the sign = 3 feet
Length of the sign's shadow = Length of the tree's shadow = 20 feet
Distance from the base of the sign to the base of the tree = 16 feet
We can set up the proportion as follows:
(Height of the sign) / (Length of the sign's shadow) = (Height of the tree) / (Length of the tree's shadow)
Plugging in the values we know:
3 / 20 = h / 20
To solve for "h", we can cross-multiply:
3 * 20 = h * 20
60 = 20h
Now, divide both sides by 20 to isolate "h":
60 / 20 = h
3 = h
Therefore, the height of the tree is 3 feet.