Use similar triangles to solve. a person who is 6 feet tall is standing 132 feet from the base of a tree, and the tree casts a 143 foot shadow. the person's shadow is 11 feet in length. what is the height of the tree?

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Mathematics

Maribel

5 April, 22:42

Use similar triangles to solve. a person who is 6 feet tall is standing 132 feet from the base of a tree, and the tree casts a 143 foot shadow. the person's shadow is 11 feet in length. what is the height of the tree?

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Terry Harrington · Answer 1

Let the height of tree be denoted as AB and the shadow cast by the tree be BE. ABE is the triangle formed the tree, rays and the ground. Let the height of the person be CD and the length of his shadow be DE. CDE is the triangle formed by the person, rays and the ground. We have two triangles. Both the person and the tree stand vertically over the horizontal ground, therefore they make 90 degrees with the ground. The angle formed at the ground is the same for the both the triangles. Therefore, by AA similarity the two triangles are similar. We know that if two triangles are similar, then their sides are proportional. Therefore, AB/CD = BE/DE AB/6 = 143/11 AB = (143/11) * 6 AB = 78 ft.