An equation that can be used to determine the tree's height is 22.5/8.25 = x/5.5.
The height of this tree is equal to 15 feet.
The distance of this person from the tree is equal to 14.25 feet.
<h3>What are the properties of similar triangles?</h3>In Geometry, two (2) triangles are similar when the ratio of their corresponding sides are equal in magnitude and their corresponding angles are congruent.
Additionally, two (2) geometric figures are considered to be congruent only when their corresponding side lengths are congruent and the magnitude of their angles are congruent.
Now, we can write an equation that can be used to determine the tree's height. Since the ratio of the corresponding sides of similar triangles are equal in magnitude, we have the following mathematical expression (equation):
22.5/8.25 = x/5.5
Where:
x represents the height of the tree.
<h3>How tall is the tree?</h3>22.5/8.25 = x/5.5
Cross-multiplying, we have:
8.25x = 22.5 × 5.5
8.25x = 123.75
x = 123.75/8.25
x = 15 feet.
<h3>How far is the person standing from the tree?</h3>The distance of this person from the tree can be calculated as follows;
Distance = Length of tree's shadow - Length of person's shadow
Distance = 22.5 - 8.25
Distance = 14.25 feet.
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