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7.92 inches. Others have each link 1 ft. long, making the length of the chain 100 feet. Chains are used when the territory is rough and extreme accuracy not essential.

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The tape (Fig. 156) is more convenient, less bulky, and more accurate than the chain. Tapes are usually 50 or 100 ft. long.

The chaining pins (Fig. 157) are used to mark points on the ground.

THE SCALE-DRAWING METHOD OF FINDING

UNKNOWN DISTANCES

79. Scale drawing. We have seen that distances which cannot be measured directly, such as the width of a river, or the height of a chimney, may sometimes be found by laying off a triangle congruent with a triangle having the required distance as one side. This is the congruent-triangle method of indirect measurement. When it is impossible, or inconvenient, to lay off the triangle, other methods of finding the unknown distance are needed. The following example illustrates a method known as the scale-drawing method.

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Let it be required to find how far it is from one corner

of the classroom to the
opposite corner.

Solution: Two consecu-
tive sides of the room are
measured and found to be
20 ft. and 30 ft. long, re-

spectively (Fig. 158). Let the side of a small square on squared paper represent 1 foot (Fig. 159).

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Fig. 158

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Draw BC=6 cm., to represent the 30 ft. side.
Draw BA=4 cm., to represent the 20 ft. side.
Complete the rectangle ABCD.

Then ABCD is a scale drawing of the classroom floor with dimensions proportionally smaller than the actual dimensions. Thus, a length in the drawing equal

to a centimeter represents a length of 5 ft. of the floor. The drawing is then said to be made to the scale: 1 cm.=5 ft.

The distance from A to C in the drawing is found by measurement to be about 7.2 cm., the 2 being estimated and therefore doubtful. The actual distance is (7.2X5) ft., or 36 feet approximately.

Summary: The preceding method of finding the distance AC involves the following steps:

1. Lines and angles related to the required distance are measured. In the example above we measured AB, BC, and LB (Fig. 159).

2. A convenient scale is selected, measured lines are drawn to scale on squared paper, and the measured angles are drawn where they are needed to complete the figure.

3. The line representing the required distance, as AC, is then drawn and measured.

4. The measurement obtained from the scale drawing is changed to the actual length.

Knowing how to draw to scale is important as it enables us to understand plans of land made by the surveyor, the maps used in geography, and the blue prints of the architect. The problem above shows that by measuring lines on the scale drawing we can determine the lengths of parts of the objects which the drawing represents, or the distances which cannot be measured directly. For this reason the scale must always be stated on the drawing.

80. Diagonal. A segment which joins two vertices of a polygon which do not lie in the same side is a diagonal of the polygon.

EXERCISES

1. Find the scale on a map of the state in which you live.

2. In the design of the hand mirror (Fig. 160) determine the actual lengths indicated by the dotted lines.

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3"

3. Find the scale used in the diagram (Fig. 161).

Ź" 4. Draw the design (Fig. 161) in actual size on a piece of heavy cardboard, cut along the solid lines, and then bend along the

3" dotted lines. By joining the edges together by means of the flaps, a use

Fig. 161 ful envelope case will be obtained. This may be mounted on a board 7}"X3".

11"

In working out the exercises below follow the directions given in $79.

5. A baseball diamond is of the form of a square whose side is 90 ft. long. Make a scale drawing of the diamond and find the direct distance of a throw from first to third base.

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