The given triangles are special triangles because they contain a 90° angle. So, we can use the Pythagorean theorems. However, we have to know at least two data. If we use the smaller triangle, we can solve the rest of the quantities. But since the left triangle only has the base measuring 8 feet, we can't rely on Pythagorean theorems. The only way to solve this is to assume that both triangles are similar so that we can apply ratio and proportion.
By using ratio and proportion, we assume that the ratio of the actual height of the object to the length of the shadow is equal for both similar triangles. So, we use the figure for the mailbox as our basis: Let's denote x as the height of the tree.
x/8 = 3/5
Solving for x,
x = 4.8 feet.
Therefore, the height of the tree is 4.8 feet.
