Going off on a tangent..... Eddie has an interesting wind guage that he can see from his office window. The wind guage is a helium balloon anchored to a wire. The ends of the wire are anchored to pegs in the ground (the wire is longer than the distance between the pegs). If there's no wind, the balloon sits midway between the pegs, pulling upward on the wire. If one were looking at the the wind guage, the wire and the ground between the pegs would form a triangle. When the wind blows, the triangle can tilt one way or the other. Depending upon the speed and direction of the wind, the balloon can slide along the wire, creating a triangle of a different shape. In fact, if the wire blows hard enough in the proper direction, the balloon can lie flat on the ground, so the wires just lay on top of each other, one side obviously much shorter than the other. Eddie watches this every day, and eventually starts recording details to see if he can figure out what each angle means in terms of wind speed. The very first day, he notices something very interesting. If he adds the tangents of all 3 angles in the triangle formed by the balloon wires and the ground between the pegs, they add up to 6.5. What product is obtained if the tangent of all 3 angles are multiplied together? Bonus questions: If the pegs are 100 inches apart, what is the minimum length of wire needed (plus or minus 1 inch) for the sum of the tangents to equal 6.5? The maximum length (plus or minus 1 inch)?