is example,

as 10 is to 20 so 8 is to the distance from B to X, which would be 16.
Having discovered the distance between A and B in the case given, to be
4 feet, take this from the distance between B and X and the result will
give the width of the stream, which is 12 feet.

[Illustration: Diagram A. To Measure Width of Stream or Road]

It may not be always necessary to use the line A--B but if the edge of
the stream or road is crooked it is necessary in order to make B--D a
straight line at right angles to A--X.

In calculating a height, as that of a tree, house or tower, the
triangles can again be used, as shown in diagram B. Choose a level strip
of ground; pace the distance in a straight line, from the base of the
tree A, or tower, to a point some distance from the tree, and plant a
pole or stake say 5 feet high B; continue pacing the straight line to
the point where, lying down with eyes level with the tree base, the top
of the tree can be seen on a line with the top of the pole; plant here
stake C. The height of the tree AA' will be to the length of the
distance from C to A as the height of the pole, BB' is to the distance
between B and C. A Scout can stand in the place of the stake B.

[Illustration: Diagram B. To Measure Height of Tree, Etc.]

[Illustration: Diagram C. To Measure Height with a Mirror]

There are other ways of determining height. As shown in the diagram C,
place a mirror (M) horizontally on the ground reflector side up, some
distance from the base of the object to be measured, in this case a
tent. Walk backward from the mirror in a straight line until the top of
the tent pole can be seen in it. The problem will read in this way: the
distance from the mirror to your heels (MS) is to the distance from your
heels to your eyes (GS) as the distance from the mirror to the base of
the object (MT) is to the height of the object (TT'). Water in a dark
pan or tray or a pool on a still day will answer for a mirror.

[Illustration: Diagram D. To Test a Right Angle]

A right angle can be tested by measuring off 3 feet on one side of the
corner and 4 feet on the other side, as shown in diagram d. If the
distance between the two points is 5 feet the angle is true; if not 5
feet move one point as much as is necessary to make 5 feet.

South American natives estimate height fairly correctly by turning the
back to the object, walking straight away from it to the point where the
top of the object can be se