Adding Vectors Using a Ruler and a Protractor

 

The yellow line represents the distance in which we are interested. The measurement from the San Buenaventura Mission to the Mission in Santa Barbara is 2.2 centimeters. Convert this to miles. The map used in this example has a scale of 2.0 cm = 20 miles. Therefore, our proportion will be:

2.0 cm / 20 miles = 2.5 cm / x miles

x = 25.1 miles

Now, if we measure the angle between the yellow line and a line which is due west, we get about 23 degrees. The horizontal grid lines are lines of latitude and are therefore 'east - west' lines. This yellow line is pointing slightly north of due west, so we may take the small angle we just measured and add it to 270 degrees which, as you will recall, is 'west'. The distance and bearing from San Buenaventura to Santa Barbara is 25 miles at 293 degrees. This is the journey 'as the crow flies'. If we look at the road map, just to the east (right) of the inset which says "See map page 9", we see a vertical green line which is the designation for a county line. Usually, county lines are N-S (or E-W). This will give you a basis for determining an E-W line

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An Assignment: Measure and record the distances between selected locations. Measure the distances in inches or centimeters and show how to convert then to miles or kilometers. Be sure to name the locations which you choose. If possible, measure the appropriate angles to find the compass headings from one location to another.


Note: Comparing measurements from 4 different maps for these two locations gives the following results: 25.0 miles, 26.0 miles, 26.9 miles, 25.0 miles. The average is 25.7 miles. One source of error involves the marking on the individual maps. Two measurements were between the two missions and two were between the two cities in which the missions reside.