Please explain. I was previously led to believe that only the 30-60 and 45-45 triangles can be calculated from knowledge of the length of 1 side. Otherwise 2 sides were necessary and thus the angle irrelevant.
Ken,
Yes, the 30/60/90 and 45/45/90 triangles make it very easy to calculate the length of any side knowing only the length of one side. But that is not the problem statement here. Trigonometry says that you can solve for the length of any side of a right triangle knowing either 1) the lengths of the other two sides (by using Pythagorean Theorem), or 2) the length of one side and the value of one of the other two angles (those that are not the right angle).
Since we are given the (overhanging) angle of the subject pitch of the Leaning Tower as 110 degrees, we know the interior of that angle is 70 degrees. And since the 200-foot side is known, and that side must be perpendicular to the ground line, we have all that is needed to solve by trig (one known side and two known angles).
Now that we are on page 3, maybe it's time to point out that he's actually closer than 72.7 feet to the wall at the end of his line. Just not horizontally.
Perpendicular distance from the wall = 72.8 * sin 70 = 68.4 feet from the wall at the end of his rope.