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Geometry QuestionHere is a very interesting geometry question that I ask my students.
Using a piece of paper, a pencil, and a ruler, draw a 4 degree angle.
Draw a right angled triangle with the adjacent ~14.3 times longer than the opposite..the angle should be 4 degrees?
Eg. a 14.3 cm side, with a 1 cm side at 90 degrees to it..with a line between the points making up a right angled triangle. Should be close enough to four degrees
Sounds right. Where did you get the 14.3:1 ratio? Can you derive this ratio without using a tangent table by using one geometry rule?
sin(4 deg.)=(opposite side)/(hypotenuse)
sin of four degrees pretty much needs to be done with a calculator... 0.0697564737=(opposite side)/(hypotenuse) we want to draw a simple triangle so lets make the opposite side 1cm: 1/0.0697564737=hypotenuse hypotenuse=14.34
No trig tables may be used. There is a much easier way. In spudding is there ever a need to figure angles?
Yes.
Does that thing kinda look like a big cat to you?
Can you make a 4 degree angle with paper, pencil, and ruler without using trig tables?
Yes.
1) For an angle that small, then tan (x) will be close to X, if using radians. A 1 to (4/180*pi) ratio will give an angle of 4.003 degrees. 2) If you want a better approximation for larger angles, it's strictly sin(x) which is close to x when X is small, so using the cos(x)<sup>2</sup> + sin(x)<sup>2</sup> = 1 rule, you can get a better approximation of tan(x) that's 95% accurate up to about half a radian. 3) If you're really in a silly mood, you can derive tan(x) by solving the sequences sin(x) = x  x<sup>3</sup>/3! + x<sup>5</sup>/5!  x<sup>7</sup>/7! + x<sup>9</sup>/9!  ...... cos(x) = 1  x<sup>2</sup>/2! + x<sup>4</sup>/4!  x<sup>6</sup>/6! + x<sup>8</sup>/8!  ...... as far as you can be bothered (or one of them, and find the other via cos(x)<sup>2</sup> + sin(x)<sup>2</sup> = 1) Then feed them into tan(x) = sin(x)/cos(x) and go from there. However, they invented these wonderful things called protractors and calculators, so normally, I don't bother.
Does that thing kinda look like a big cat to you?
Is 4 degrees just pulled out of a hat or is it special? I suspect that there's a trick involved specific to that angle, and that you're not looking for a brute force solution using a Taylor series or anything like that.
Excellent!
The nice thing to remember is that 1 radian is 57.3 degrees. Therefore 1 part in 57.3 is 1 degree. Go out 57.3 units and up 1 and you have 1 degree. Very simple to do. I designed and built a truck wheel alignment business based on this relationship. We aligned fire engines at the fire stations. Next challenge: How to measure the camber angle of a tire/wheel to within 1/10 of a degree with a homemade $5 device?
Seems optimistic. You might get a precision of 0.1 degrees, but I don't think you're likely to get an accuracy of 0.1 degrees.
Does that thing kinda look like a big cat to you?
I can get accuracy of 0.1 degree.
I will leave this topic open since it has received quite a bit of feedback, is so very slightly related to spudguns and so you don't post another topic like this because we locked your previous ones.
However, Boytonstu, please don't post another topic like this (math related, pointless, irrelevant). You can come up with as many examples of other topics that weren't locked as you want but at the end of the day the decision is down to the Moderator(s). Not every topic that should be locked will be locked, there are a few reasons for this, some of which you may be unaware of as the reasons could be discussed over PM. This topic itself could end up being an example of a topic that wasn't, but should've been, locked. So, from now on, Boyntonstu, keep your NSGRD topics within the guidelines. If you purposely post a topic that falls through the cracks just to prove a point, well, we'll probably lock it just to prove we can. Usually I wouldn't go out of my way to say all this but seeing as we locked a math related topic of yours yesterday for being irrelevant and then today (NZ time), you post another math related topic, I feel you're just doing it to try and prove a point.
 
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