To Measure the Height of a Tree
There is a very easy way to measure the height of a wall or tree - a method that anyone can use if he or she can do a problem in simple proportion. It is necessary that the sun should be shining at the time and that a shadow should be cast. That is all that is required to do this easy problem.
Suppose that you wish to measure a tree and that the sun is shining; then the shadow of the tree is cast on the ground. You must measure the distance from the tip of the shadow to the place right under the top of the tree. If the top point of the tree is right above the middle of the trunk, you must calculate half the diameter of the trunk in making your measurements.
Suppose that the distance from the point of the shadow to the trunk of the tree is 40 feet, and that the tree is 2 feet thick. Then the total distance is 41 feet (40 feet + half the diameter of the tree). Now take a stick of which you know the exact length. Suppose that it is 3 feet long.
Hold this upright with one end on the ground, and notice how far its shadow extends. You will find, perhaps, that it is 6 feet long. Multiply the length of the tree’s shadow (41 feet) by the length of the stick (3 feet); divide by the length of the stick’s shadow (6 feet). This gives 20.5; that is, the tree is 20.5 feet high.
You can also get the answer, though not quite so correctly, by seeing how many steps it takes to go from the edge of the shadow to the tree, being careful to make your steps as nearly equal as possible. Then, after measuring the length of one step, multiply its length by the number of steps. This is the distance from the shadow’s edge to the tree.
Be sure that you take the distance to a point right under the highest point. If it is a church spire, for example, make allowance for the distance between the wall up to which you measure and the center of the church tower topped by the spire.
