Final answer:
Using similar triangles, the height of the eucalyptus tree is found to be 4.2 feet tall, given the ratio of the 3-foot red kangaroo's height to its 5-foot shadow and the tree's 7-foot shadow.
Step-by-step explanation:
On a sunny day, a 3-foot-tall red kangaroo casts a 5-foot-long shadow. At the same time, the shadow of a nearby eucalyptus tree is 7 feet long. To find the height of the tree, we can use similar triangles.
The kangaroo's height of 3 feet and shadow of 5 feet form a ratio. The tree's height (which we do not know) and shadow of 7 feet will have the same ratio because the sun's angles are the same for both the kangaroo and the tree.
We can write the proportion as:
Kangaroo's Height / Kangaroo's Shadow = Tree's Height / Tree's Shadow
So, we can say:
3 feet / 5 feet = Tree's Height / 7 feet
Cross-multiply to solve for the tree's height:
(3 feet) * (7 feet) = (Tree's Height) * (5 feet)
21 feet2 = (Tree's Height) * 5 feet
Divide both sides by 5 feet to isolate Tree's Height:
Tree's Height = 21 feet2 / 5 feet
Tree's Height = 4.2 feet
Therefore, the eucalyptus tree is 4.2 feet tall.