But it is seldom so easy, and the good old rule of the triangle can be safely counted on: Get a hundred or more feet from your tree, on open ground, as nearly as possible on the level of its base. Set up a ten-foot pole (A B, page 65). Then mark the spot where the exact line from the top of the tree over the top of the pole touches the ground (C). Now measure the distance from that spot (C) to the foot of the ten-foot pole (B); suppose it is twenty feet. Measure also the distance from that spot (C) to the base of the tree (D); suppose it is one hundred and twenty feet, then your problem is:
20 : 10 :: 120 : x = 60
i.e., if at that angle twenty feet from the eye gives ten feet elevation, one hundred and twenty feet must give sixty.
To make a right angle, make a triangle whose sides are exactly six, eight, and ten feet or inches each (or multiples of these). The angle opposite the ten must be a true right angle.
To make a right angle
There are many ways of measuring distance across rivers, etc., without crossing. The simplest, perhaps, is by the equilateral triangle. Cut three poles of exactly equal length; peg them together into a triangle. Lay {65} this on the bank of the river so one side points to some point on the opposite bank. Drive in three pegs to mark the exact points of this triangle (A,B,C). Then move it along the bank until you find a place (F,E,G) where its base is on line with the two pegs, where the base used to be, and one side in line with the point across the river (D). The width of the river is seven eighths of the base of this great triangle.
Another method is by the isosceles triangle. Make a right-angled triangle as above, with sides six, eight, and ten feet (A,B,C); then, after firmly fixing the right angle, cut down the eight-foot side to six feet and saw off the ten-foot side to fit. Place this with the side D B on the river bank in line with the sight object (X) across. Put three pegs to mark the three {66} corner places. Then take the triangle along the bank in the direction of C until C' D' are in line with the sight object, while B' C' is in line with the pegs B C. Then the length of the long base B C' will equal the distance from B to X.
