Method of Applying the Triangle Measure
"Near the end of the season our boy announced the height of our tall maple tree to be 33 ft.
"'Why, how do you know?' was the general question.
" 'Measured it.' "'How?'
" 'Foot rule and yardstick.'
" 'You didn't climb that tall tree?' his mother asked anxiously.
" 'N o'm; I found the length of the shadow and measured that.'
"'But the length of the shadow changes.'
" 'Yes'm; but twice a day the shadows are just as long as the things themselves. I've been trying it all summer. I drove a stick into the ground, and when its shadow was just as long as the stick I knew that the shadow of the tree would be just as long as the tree, and that's
The above paragraph appeared in one of the daily papers which come to our office. The item was headed, "A Clever Boy." Now we do not know who this advertised boy was, but we knew quite as clever a boy, one who could have got the approximate height of the tree without waiting for the sun to shine at a particular angle or to shine at all for that matter. The way boy No. 2 went about the same problem was this: He got a stick and planted it in the ground and then cut it off just at the level of his eyes. Then he went out and took a look at the tree and made a rough estimate of the tree's height in his mind, and judging the same distance along the ground from the tree trunk, he planted his stick in the ground. Then he lay down on his back with his feet against the standing stick and looked at the top of the tree over the stick.
If he found the top of stick and tree did not agree he tried a new position and kept at it until he could just see the tree top over the end of the upright stick. Then all he had to do was to measure along the ground to where his eye had been when lying down and that gave him the height of the tree.
'The point about this method is that the boy and stick made a right-angled triangle with boy for base, stick for perpendicular, both of the same length, and the "line of sight" the hypotenuse or long line of the triangle. When he got into the position which enabled him to just see the tree top over the top of the stick he again had a right-angled triangle with tree as perpendicular, his eye's distance away from the trunk, the base, and the line of sight the hypotenuse. He could measure the base line along the ground and knew it must equal the vertical height, and he could do this without reference to the sun. It was an ingenious application of the well known properties of a right-angled triangle. --Railway and