ACT Preparation / Unit 13 ACT 1221 worked example, 60 to 90 seconds
Similar Triangles in the World
The idea
Similar triangles measure what cannot be reached, in three steps. First, sketch the two triangles, often formed by objects and their shadows, with the right angles marked. Second, argue similarity: the sun's rays meet the ground at the same angle for both objects at the same moment, and both objects stand upright, so AA holds. Third, set height over shadow equal to height over shadow and solve.
In practice
Worked example: a 1.8-meter post casts a 2.4-meter shadow while a tree casts a 16-meter shadow at the same time. The proportion 1.8/2.4 = h/16 gives 2.4h = 28.8, so the tree is 12 meters tall.
Where people slip
Keep the same order on both sides: height over shadow equal to height over shadow. Mixing them, as in 1.8/2.4 = 16/h, gives a different and wrong height.
Your place on the trail
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