Geometry/Algebra 2

The pitch of a roof is equivalent to the hypotenuse of a triangle. The 11/18 in an 11/18 pitch, is the slope of the pitch, and we know that the slope is the rise of the run. With the knowledge that the slope is rise/run, we can deduce that the two legs are 11 and 18, with 11 being the rise and 18 being the run. Then from there, it is quite simple to find the angle of elevation. To find the angle of elevation you first set up the tangent equation: Tan A=11/18. Then you multiply each side by the inverse tangent: A= tan^-1 (11/18). Then you will get that the angle A is equal to 31 degrees. Next, we had to find the "rafter line" if the full length of the "run" is 22ft. This was pretty easy to figure out, first, I had to set up the equation: Cos31=11/x. I chose to use the Cos equation because we were trying to find the length of the rafter which is equivalent to the hypotenuse of a triangle, and we were given the adjacent leg. Next, we simply solved the equation: x=Cos

The grade of a road is the tangent of the angle of that surface to the horizontal. If the grade is 0% then there is no slope, but the greater the % the higher/steeper the degree of tilt is. Knowing the grade of a road is important for cars because they have something called the gradeability. The gradeability of a car is the highest grade a car can go at a certain speed. So if the grade is high the driver then knows that they have to go a greater speed to prepare for the steep hill. The grade of a road is equal to the slope of a line. Also, the grade of a road is equivalent to the hypotenuse of a triangle, so if we can use trigonometry to find the hypotenuse we can use trigonometry to find the grade of a road.

Fractals were discovered in 1975 by a Polish man by the name of Benoît Mandelbrot, and when I say discovered I mean finally put into words. Benoît Mandelbrot defined a fractal as a geometric shape that when split into smaller parts, those parts would be exact replicas of the first shape. The word fractal comes from the Latin word fractus which means "broken" or "fractured". The idea of fractals had been around for a very long time before Benoît Mandelbrot, but he was the first to actually realize how amazing they were. Mandelbrot's first started researching how fractals can be found in nature. His first report was about how long the coast of Britain actually was. Before Benoît Mandelbrot, many mathematicians and philosophers had studied the idea of recursive self-similarity. But it wasn't until Mandelbrot solidified hundreds of years of thought and mathematical development and created the term fractal. After Mandelbrot, in 1980, an American by the name of Lo