The scale of the replica is 30 : 1.
b. Since the scale of the replica is 30: 1, this means
7-7 Scale Drawings and Models
that the actual hat is 30 times wider than the replica.
9. SCALE MODELS The hat atop the Eiffel Tower
replica is made of steel. It measures 4.5 feet high
and has a brim that is 10 feet wide . The brim of a
similar hat is 4 inches wide.
16. MODEL TRAINS Model train scales are
standardized across the industry. The most popular
scale is 1:87. The recommended vertical clearance
for a tunnel in this scale is between
inches and
inches. To the nearest foot, find the range of
vertical clearance needed for a real train.
SOLUTION: a. What is the scale of the replica? b. How many times as wide as the actual hat is the
replica?
The lower range of the model is
inches. So, for every inch on the actual measure a, let the model m
be 87 inches. Write this as an equation.
SOLUTION: a. To find the scale of the replica, find the ratio of the
width of the actual hat to the width of the replica.
Repeat this process for the higher range of
The scale of the replica is 30 : 1.
. b. Since the scale of the replica is 30: 1, this means
that the actual hat is 30 times wider than the replica.
16. MODEL TRAINS Model train scales are
standardized across the industry. The most popular
scale is 1:87. The recommended vertical clearance
for a tunnel in this scale is between
inches and
inches. To the nearest foot, find the range of
vertical clearance needed for a real train.
SOLUTION: The range of vertical clearance needed for a real
train would be between 17 and 23 feet.
17. ROCKETS Peter bought a
The lower range of the model is
inches. So, for every inch on the actual measure a, let the model m
be 87 inches. Write this as an equation.
scale model of the
Mercury-Redstone rocket.
a. If the height of the model is 7 inches, what is the
approximate height of the rocket?
b. If the diameter of the rocket is 70 inches, what is
the diameter of the model? Round to the nearest half
inch.
SOLUTION: a. Let x be the approximate height of the rocket.
Form a proportion and solve for x. Repeat this process for the higher range of
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a. GEOMETRIC Draw right
The range
of vertical
7-7 Scale
Drawings
and clearance
Models needed for a real
train would be between 17 and 23 feet.
17. ROCKETS Peter bought a
scale model of the
with the right angle at vertex B. Draw altitude
Draw right with right angle N and altitude
and right
with right angle X and altitude
b. TABULAR Measure and record indicated angles
in the table below.
Mercury-Redstone rocket.
a. If the height of the model is 7 inches, what is the
approximate height of the rocket?
b. If the diameter of the rocket is 70 inches, what is
the diameter of the model? Round to the nearest half
inch.
SOLUTION: a. Let x be the approximate height of the rocket.
Form a proportion and solve for x. c. VERBAL Make a conjecture about the altitude of
a right triangle originating at the right angle of the
triangle.
The height of the rocket is approximately 84 feet. b. Let x be the diameter of the model. (12 feet = 144 inches)
SOLUTION: a. When drawing your triangles, it is important that
you use a straight edge and a protractor, so that you
measurements are accurate. Follow the directions
carefully and label the triangles as directed. Form a proportion and solve for x. The diameter of the model rocket is approximately
0.5 inches. 20. MULTIPLE REPRESENTATIONS In this
problem, you will explore the altitudes of right
triangles.
a. GEOMETRIC Draw right
with the right angle at vertex B. Draw altitude
Draw right with right angle N and altitude
and right
with right angle X and altitude
b. TABULAR Measure and record indicated angles
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in the table below.
b. Carefully measure the angles of each triangle and
record the measurements in the table below. Pay
attention to any patterns you see. Sample answer are given.
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b. Carefully measure the angles of each triangle and
recordDrawings
the measurements
in the table below. Pay
7-7 Scale
and Models
attention to any patterns you see. Sample answer are given.
c. Notice how the angles in each triangle formed by
the altitude from the right angle vertex are the same
as the original triangle. What does this mean about all
three triangles?
The altitude originating at the right vertex of a right
triangle divides the triangle into three similar
triangles.
21. ERROR ANALYSIS Felix and Tamara are building
a replica of their high school. The high school is 75
feet tall and the replica is 1.5 feet tall. Felix says the
scale factor of the actual high school to the replica is
50: 1, while Tamara says the scale factor is 1: 50. Is
either of them correct? Explain your reasoning.
SOLUTION: The scale factor of the high school and the replica
can be determined by reducing the ratio of their
heights: .
Therefore, Felix is correct. eSolutions Manual - Powered by Cognero
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