Explanation Similar triangle: Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion. In other words, similar triangles are in similar shape, however not really a similar size. A B D E = B C E F = A C D F If a line is drawn in a triangle so that it is parallel to one of the sides and it intersects the other two sides then the segments are of proportional lengths: A D D B = E C B E Portions of two triangles can be proportional: if two triangles are known to be similar then the perimeters are proportional to the measures of corresponding sides. Calculation: Given: The shadow cast by a tree = 8 ft 3 in The height of a person = 5ft 1 0 in The shadow cast by a person = 2 ft 7 in Let h represents the height of the building. The tree and person are vertical. So, the shadows are horizontal. In both cases, a right triangle is formed by the tip of the shadow and the base and top of the tree or person. The angle at the top of the right triangle is determined by the angle of the sun, so it's the same for both. Thus, the two triangles are similar, and corresponding sides are in corresponding ratios. To find h : We have to identify the two triangles. The two triangles are Δ A C D and Δ B C E . We have to determine that two triangles are similar. If we know that the triangles are right angles, we can easily identify similar triangles. Since then the triangles are similar, if one of the acute angles of one triangle has the same measure as an acute angle of the other. Δ A C D and Δ B C E both have a right angle. Therefore, Δ A C D ∼ Δ B C E . Then, we have to set up a proportion using corresponding parts of similar triangles

13th Edition

ISBN: 9781285697734

Author: karl J. smith

Publisher: Cengage Learning US

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Chapter 7.4, Problem 51PS

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The height of a tree which casts a shadow of 8 ft 3 in.

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Chapter 7.4, Problem 50PS

Chapter 7.4, Problem 52PS

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Ch. 7.1 - Is the woman in the figure a young woman or an old...Ch. 7.1 - Is the fly in the Figure 7.11 on the cube or in...Ch. 7.1 - Prob. 3PS Ch. 7.1 - Prob. 4PS Ch. 7.1 - Prob. 5PS Ch. 7.1 - Prob. 6PS Ch. 7.1 - Prob. 7PS Ch. 7.1 - Prob. 8PS Ch. 7.1 - Prob. 9PS Ch. 7.1 - Prob. 10PS

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The height of a tree which casts a shadow of 8 ft 3 in.

Solution Summary: The author explains that two triangles are similar if their angles are congruent and the corresponding sides are in proportion.

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The height of a tree which casts a shadow of 8 ft 3 in.

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Chapter 7 Solutions