Use triangle congruence and similarity criteria to solve problems and prove geometric relationships.
Solve an indirect measurement problem with triangle similarity
Problem
Use triangle similarity to solve this indirect measurement problem: A \(5\text{-}\text{ft}\) person casts a \(6\text{-}\text{ft}\) shadow, and a building casts a \(48\text{-}\text{ft}\) shadow. How tall is the building?
Indirect measurement works because the person-shadow and building-shadow triangles share the same shape. We’ll justify AA from vertical objects, horizontal ground, and parallel sunlight, compare height to shadow in one consistent order, solve the proportion, and check the units and ratio.
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