Of course, none of us had studied trigonometry, but Uncle Ed devised a
very simple method by which we could determine distances quite accurately
without much figuring.

"If you will tell me the length of one side of a triangle and the angles
it makes with the other two sides," said Uncle Ed, "I'll tell you the
length of the other two sides and the size of the third angle. This is how
I will do it:

"Say the line is 6 inches long and one angle is 35 degrees, while the
other is 117 degrees. Let us draw a 6-inch straight line. This we will
call our base line. Now we will place the base edge of our protractor on
the base line with its center at the right hand end of the line. At the 37
degree mark we will make a dot on the paper so, and draw a line from the
right hand end of the base line through this dot. Now we will do the same
thing at the opposite end, making a dot at 107 degrees from the line, and
draw a line from the left hand end of the base line through this dot. If
we extend these lines until they intersect, we will have the required
triangle, and can measure the two sides, which will be found to be about
12 inches and 8 inches long, and the third angle will measure just 26
degrees. It doesn't make any difference on what scale we draw the
triangle, whether it be miles, yards, feet, inches or fractions of an
inch, the proportions will be the same. If the base line had been 6
half-inches, or 3 inches long, and the same angles were used, the other
two lines would measure 12 half-inches, or six inches, and 8 half-inches,
or 4 inches. If the base line were 6 quarter-inches long, the sides would
be 3 inches and 2 inches long.

"Now, for example, I am going to measure the distance to that tree over
there. Get out your chain and measure off a straight line 10 feet long.