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 = 4 ft 5 in The height of a person = 5 ft 9 in The shadow cast by a person = 3 ft 1 0 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. Since the given triangles are similar, the ratio A C ¯ : A D ¯ is equal to B C ¯ : B E ¯

Nature of Mathematics (MindTap Course List)

13th Edition

ISBN: 9781133947257

Author: karl J. smith

Publisher: Cengage Learning

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Question

Chapter 7.4, Problem 52PS

To determine

The height of a tree which casts a shadow of 4 ft 5 in.

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Chapter 7 Solutions

Nature of Mathematics (MindTap Course List)

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

Ch. 7.1 - Prob. 11PS Ch. 7.1 - Prob. 12PS Ch. 7.1 - Prob. 13PS Ch. 7.1 - Prob. 14PS Ch. 7.1 - Prob. 15PS Ch. 7.1 - Prob. 16PS Ch. 7.1 - Prob. 17PS Ch. 7.1 - Prob. 18PS Ch. 7.1 - Use the illustration in Figure 7.12 to draw the...Ch. 7.1 - Prob. 20PS Ch. 7.1 - Prob. 21PS Ch. 7.1 - Prob. 22PS Ch. 7.1 - Prob. 23PS Ch. 7.1 - Prob. 24PS Ch. 7.1 - Prob. 25PS Ch. 7.1 - Prob. 26PS Ch. 7.1 - Prob. 27PS Ch. 7.1 - Carry out the constructions requested in Problems...Ch. 7.1 - Prob. 29PS Ch. 7.1 - Prob. 30PS Ch. 7.1 - Prob. 31PS Ch. 7.1 - Prob. 32PS Ch. 7.1 - Prob. 33PS Ch. 7.1 - Prob. 34PS Ch. 7.1 - Prob. 35PS Ch. 7.1 - Prob. 36PS Ch. 7.1 - Prob. 37PS Ch. 7.1 - Prob. 38PS Ch. 7.1 - Prob. 39PS Ch. 7.1 - Prob. 40PS Ch. 7.1 - Prob. 41PS Ch. 7.1 - Prob. 42PS Ch. 7.1 - Prob. 43PS Ch. 7.1 - Prob. 44PS Ch. 7.1 - Prob. 45PS Ch. 7.1 - Prob. 46PS Ch. 7.1 - Prob. 47PS Ch. 7.1 - Prob. 48PS Ch. 7.1 - Prob. 49PS Ch. 7.1 - Prob. 50PS Ch. 7.1 - Prob. 51PS Ch. 7.1 - Study the patterns shown in Figure 7.13. 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At the same...Ch. 7.4 - Prob. 48PS Ch. 7.4 - Prob. 49PS Ch. 7.4 - Prob. 50PS Ch. 7.4 - Prob. 51PS Ch. 7.4 - Prob. 52PS Ch. 7.4 - Prob. 53PS Ch. 7.4 - Prob. 54PS Ch. 7.4 - Prob. 55PS Ch. 7.4 - Suppose a 6- ft person wishes to determine the...Ch. 7.4 - Prob. 57PS Ch. 7.4 - Prob. 58PS Ch. 7.4 - Prob. 59PS Ch. 7.4 - Prob. 60PS Ch. 7.5 - Prob. 1PS Ch. 7.5 - Prob. 2PS Ch. 7.5 - Prob. 3PS Ch. 7.5 - Prob. 4PS Ch. 7.5 - Prob. 5PS Ch. 7.5 - Prob. 6PS Ch. 7.5 - Prob. 7PS Ch. 7.5 - Prob. 8PS Ch. 7.5 - Prob. 9PS Ch. 7.5 - Prob. 10PS Ch. 7.5 - Prob. 11PS Ch. 7.5 - Prob. 12PS Ch. 7.5 - Prob. 13PS Ch. 7.5 - Prob. 14PS Ch. 7.5 - Prob. 15PS Ch. 7.5 - Prob. 16PS Ch. 7.5 - Prob. 17PS Ch. 7.5 - Prob. 18PS Ch. 7.5 - Prob. 19PS Ch. 7.5 - Prob. 20PS Ch. 7.5 - Prob. 21PS Ch. 7.5 - Prob. 22PS Ch. 7.5 - Prob. 23PS Ch. 7.5 - Prob. 24PS Ch. 7.5 - Prob. 25PS Ch. 7.5 - Prob. 26PS Ch. 7.5 - Prob. 27PS Ch. 7.5 - Prob. 28PS Ch. 7.5 - Prob. 29PS Ch. 7.5 - Prob. 30PS Ch. 7.5 - Prob. 31PS Ch. 7.5 - Prob. 32PS Ch. 7.5 - Prob. 33PS Ch. 7.5 - Prob. 34PS Ch. 7.5 - Prob. 35PS Ch. 7.5 - Prob. 36PS Ch. 7.5 - Prob. 37PS Ch. 7.5 - Prob. 38PS Ch. 7.5 - Prob. 39PS Ch. 7.5 - Prob. 40PS Ch. 7.5 - Prob. 41PS Ch. 7.5 - Prob. 42PS Ch. 7.5 - Prob. 43PS Ch. 7.5 - Prob. 44PS Ch. 7.5 - Prob. 45PS Ch. 7.5 - Prob. 46PS Ch. 7.5 - Prob. 47PS Ch. 7.5 - Level 2 If the angle from the horizontal to the...Ch. 7.5 - Prob. 49PS Ch. 7.5 - Prob. 50PS Ch. 7.5 - Prob. 51PS Ch. 7.5 - Prob. 52PS Ch. 7.5 - Prob. 53PS Ch. 7.5 - Prob. 54PS Ch. 7.5 - Prob. 55PS Ch. 7.5 - Prob. 56PS Ch. 7.5 - Prob. 57PS Ch. 7.5 - Prob. 58PS Ch. 7.5 - Prob. 59PS Ch. 7.5 - Problem solving Level 3 a. If the distance from...Ch. 7.6 - Prob. 1PS Ch. 7.6 - Prob. 2PS Ch. 7.6 - Prob. 3PS Ch. 7.6 - Prob. 4PS Ch. 7.6 - Prob. 5PS Ch. 7.6 - Prob. 6PS Ch. 7.6 - Prob. 7PS Ch. 7.6 - Prob. 8PS Ch. 7.6 - Prob. 9PS Ch. 7.6 - Prob. 10PS Ch. 7.6 - Prob. 11PS Ch. 7.6 - Prob. 12PS Ch. 7.6 - Name the geometry Euclidean, elliptic, or...Ch. 7.6 - Prob. 14PS Ch. 7.6 - Prob. 15PS Ch. 7.6 - Prob. 16PS Ch. 7.6 - Prob. 17PS Ch. 7.6 - Prob. 18PS Ch. 7.6 - Prob. 19PS Ch. 7.6 - Prob. 20PS Ch. 7.6 - Prob. 21PS Ch. 7.6 - Prob. 22PS Ch. 7.6 - Prob. 23PS Ch. 7.6 - Prob. 24PS Ch. 7.6 - Prob. 25PS Ch. 7.6 - Prob. 26PS Ch. 7.6 - Prob. 27PS Ch. 7.6 - Prob. 28PS Ch. 7.6 - Consider the top, front, and side views as shown...Ch. 7.6 - Prob. 30PS Ch. 7.6 - Prob. 31PS Ch. 7.6 - Prob. 32PS Ch. 7.6 - Prob. 33PS Ch. 7.6 - Prob. 34PS Ch. 7.6 - Prob. 35PS Ch. 7.6 - Prob. 36PS Ch. 7.6 - Prob. 37PS Ch. 7.6 - Prob. 38PS Ch. 7.6 - Prob. 39PS Ch. 7.6 - Prob. 40PS Ch. 7.6 - Prob. 41PS Ch. 7.6 - Prob. 42PS Ch. 7.6 - Prob. 43PS Ch. 7.6 - Prob. 44PS Ch. 7.6 - Prob. 45PS Ch. 7.6 - Prob. 46PS Ch. 7.6 - Prob. 47PS Ch. 7.6 - Prob. 48PS Ch. 7.6 - Prob. 49PS Ch. 7.6 - Prob. 50PS Ch. 7.6 - Prob. 51PS Ch. 7.6 - Prob. 52PS Ch. 7.6 - Prob. 53PS Ch. 7.6 - Prob. 54PS Ch. 7.6 - When is an open book a closed book? If the...Ch. 7.6 - Prob. 56PS Ch. 7.6 - Prob. 57PS Ch. 7.6 - Prob. 58PS Ch. 7.6 - Prob. 59PS Ch. 7.CR - Prob. 1CR Ch. 7.CR - Prob. 2CR Ch. 7.CR - Prob. 3CR Ch. 7.CR - Prob. 4CR Ch. 7.CR - Prob. 5CR Ch. 7.CR - Prob. 6CR Ch. 7.CR - 7. Bourbon Palace Figure 7.77 is home to the...Ch. 7.CR - Prob. 8CR Ch. 7.CR - Prob. 9CR Ch. 7.CR - Prob. 10CR Ch. 7.CR - Prob. 11CR Ch. 7.CR - Prob. 12CR Ch. 7.CR - Prob. 13CR Ch. 7.CR - Prob. 14CR Ch. 7.CR - Prob. 15CR Ch. 7.CR - Prob. 16CR Ch. 7.CR - Prob. 17CR Ch. 7.CR - Prob. 18CR Ch. 7.CR - Prob. 19CR Ch. 7.CR - Prob. 20CR

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The height of a tree which casts a shadow of 4 ft 5 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 4 ft 5 in.

Chapter 7 Solutions