Letter of the law
Problem 212 — A rose can have many names, as this month’s problem by Water Jasiolek of Livonia, Mich., demonstrates
Once again, Detective Inspector Schnoop was in pursuit of the agile spy. The spy had recruited a traitorous scientist inside one of the nation’s leading laboratories, and stood ready to receive classified data on a revolutionary new type of rocket engine. Earlier in the evening, the spy had written down his ninedigit computer password for the scientist and was about to give it to him, when Schnoop burst in on the scene.
As the spy disappeared down a dark alley a piece of paper fluttered in the breeze. On it was written:
SOLUTIONTONOVEMBER’S PROBLEM211 — You see the trees from the forest, if you answered 200 ft. Here’s the fell blow:
First, we know that the earth completes one revolution, or 360-deg turn every 24 hr. Hence the sun “moves” 15° across the sky every hour.
The sun’s path between noon and one o’- clock creates a 15° reflective angle between the top of the tree and the furthest end of the shadow (See drawing).
Since the sum of angles in a triangle must equal 180,° we subtract the right angle between the tree and the ground and the 15° angle to get 75° for the angle between the furthest end of the shadow and the base of the tree.
Now, let x be the height of the tree, ft.