This is my classmate's discussion post,
Good Morning Class,
Today I will be discussing the dimensions on the pyramid of Khufu in Egypt. According to
wondorsoftheworld.net, the pyramid has a base of about 230m with a height of 138m. First, I
divided the length of the base by 2 (ending up with 115) in order to visualize a proper right
triangle from which to calculate the slope of the side, which is 138 over 115, or 1.2. Plugging this
into the equation to find the angle, I start with 1.2=tan(Angle of tilt). To find the angle of tilt, I
plug the slope into the inverse tangent (Angle of tilt)=tan-1(1.2). Using the desmos calculator, this
gives me an inclination of about 50° for the side of the pyramid.
While not something I deal with personally, one fascinating example of real-life slopes and angles
is something in the aviation community called glide slope. This is a term that refers to the angle at
which an aircraft is supposed to descend while landing (typically 3°). This was also used by the
space shuttle as it glided down during re-entry. They used height over distance in place of rise
over run to find the slope and called it the glide ratio, which is equal to the tangent function in
regards to the angle (tan(a)=h/d). The glide angle can be calculated if the horizontal and vertical
distance of descent are known, but they could also calculate how far the shuttle would make it if
the pilot flew at a certain angle of descent as well, by swapping distance and angle in the equation
(d=h/tan(a)).
References
https://www.wonders-of-the-world.net/Pyramids-of-Egypt/Dimensions-of-the-pyramids-of-
Egypt.php
https://www.grc.nasa.gov/www/k-12/airplane/glidang.html
-Batuhan
image_17281894621660825803075.png(145.73 KB)
Upon my introduction to higher levels of mathematics, I dreaded how complicated the
subject is. Aside from that, I fail to find any relevance in such a subject. However, soon I realize
that it is just a matter of perspective. In essence, I should look way beyond the text and analyze
thoroughly what is written. A way to make mathematics on this level much easier is by visualizing
it. Reflecting on the text, the way I look through problems now is by visualizing them. Instead
of relying on texts, I try and visualize them now. For example, instead of looking at the angle of tilt
as a variable, in this application, I look over it at how the pyramid rises. In the second scenario,
instead of seeing slopes as random pieces of an equation, I look at them as a curve.
However, despite this, it is still important to understand the theoretical side of such a
subject. One cannot simply rely on simple visualizations and low levels of thinking. For example, in
terms of slope, while looking over it as the curvature of the line, one should still absorb that the
formula over it is rise divided by run. It is also important to know the identification of angles, such
as acute angle, right angle, obtuse angle, straight angle, and many more. It will also help to know
the various interractions between sine, cosine, and tange: one such example of this is that sine is a
byproduct of dividing the opposite and hypotenuse, while cos is the product of dividing adjacent to
the hypotenuse.
Respond post
Upon my introduction to higher levels of mathematics, I dreaded how complicated the
subject is. Aside from that, I fail to find any relevance in such a subject. However, soon I realize
that it is just a matter of perspective. I should look way beyond the text and thoroughly analyze
what is written. A way to make mathematics on this level much easier is by visualizing it.
Reflecting on the text, I look through problems now by visualizing them. Instead of relying
on texts, I try and visualize them now. For example, instead of looking at the angle of tilt as a
variable, in this application, I look over it at how the pyramid rises. In the second scenario, instead
of seeing slopes as random pieces of an equation, I look at them as a curve. For example, when
solving for a slope from the center to (5,10), I will visualize it first before calculating via rising
over-run (x/y), thus coming up to 10.
In your example about the pyramid, when you calculate the inclination of the side of the
pyramid, you have used the tan ratio. Because now, we don’t know the value of the Hypotenuse.
So, you used the easiest method to calculate the inclination of the side of the pyramid from the
ground. If we wish to use any of the other trigonometric ratios, we must have to calculate the
Hypotenuse of the right triangle using the Pythagorean theorem. I also followed your steps and,
using the scientific calculator, got the value below.
Angle of tilt = tan−1 (138
115)=50.1944𝑜
You did it Using the desmos calculator, and the angle is almost the same as what I got after
rounding it to the nearest degree. Your post included a nice practical scenario introducing the glide
angle. It will be very interesting to read for all of us.
However, it is still important to understand the theoretical side of such a subject. One
cannot simply rely on simple visualizations and low levels of thinking. For example, in terms of
slope, while looking over it as the curvature of the line, one should still absorb that the formula
over it is rise divided by run. It is also essential to know the identification of angles, such as acute,
right, obtuse, straight, and many more. It will also help to know the various interactions between
sine, cosine, and tan. Sine is a byproduct of dividing the opposite and hypotenuse. At the same
time, cos is the product of dividing adjacent to the hypotenuse. Thank you for sharing your
knowledge with us, and using nice practical examples.
