To find the height of an apple tree in her yard, Susan held a clipboard near her eye so that the top of the tree was viewed along one edge of the clipboard and the base of the tree was viewed along the adjacent edge. If her eye level is 4.5 feet and she is standing 15 feet from the tree, how tall is the tree?

To find the height of the apple tree in Susan's yard, we can use similar triangles.
Step 1: Identify the two similar triangles.
Triangle 1 is formed by Susan's eye height (4.5 feet), the ground, and her distance from the tree (15 feet). Triangle 2 is formed by the tree's height, the ground, and the same 15 feet distance.
Step 2: Set up the proportion.
Let 'h' be the height of the tree. The proportion can be written as:
(height of eye) / (distance from tree) = (tree height) / (distance from tree)
4.5 / 15 = h / 15
Step 3: Solve for 'h'.
Cross-multiply the proportion to solve for 'h':
4.5 × 15 = h × 15
67.5 = h × 15
Divide both sides by 15:
h = 67.5 / 15
h = 4.5
Step 4: Add Susan's eye height to find the total height of the tree.
Total tree height = height of eye + height of tree above eye level
Total tree height = 4.5 + 4.5
Total tree height = 9 feet
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