Ok, so this was the simple exercise problem I was trying to solve: "One of the legs of a right triangle has length 4. Express the length of the altitude perpendicular to the hypothenuse as a function of the length of the hypothenuse." Let's assume for a moment that h = the length of the hypothenuse, a = the length of the altitude perpendicular, x = 4, one of the legs of the triangle, and y is unknown. Because I didn't know any corners, I was trying very hard to find the solution by doing things with only the Pythagorean theorem. This turned out not to work, so I tried the law of sines, the law of cosines, and what have you. None of it worked. In the end, the solution turned out to be this: the area of the triangle A = a*h/2 = 4y/2. Therefore, a = 4y/h. Use the Pythagorean theorem to substitute y for h, and then we get a = 4*sqrt(h^2-16)/h. Easy as pie. So why do I post this? Because it was so easy, and I was unable to solve it without looking at the solutions manual. The reason for this is simple: I totally forgot about the area formula and was too focused on solving things with the Pythagorean theorem and sines and cosines. How do you avoid these kind of mistakes? Is it a simple matter of doing lots of these problems, and in time you will make less of these stupid mistakes, or do you use a certain method to make sure you're using all the 'tools' you have?