Does someone know how to prove this:
An angle of x such that 0 < x < 90 degrees can be constructed with a ruler if and only if tan(x) is a rational number.
Thanks in advance.
Hello, BrainMan!
The proof is simple in one direction . . .
An angle θ such that 0° < θ < 90°
can be constructed with a ruler if and only if tan θ is a rational number.
If $\displaystyle \tan\theta$ is a rational number $\displaystyle \frac{a}{b}$, where $\displaystyle a\text{ and }b$ are positive integers,
. . we can construct angle $\displaystyle \theta.$
Code:* R * | * | * | a * | * θ | - - * - - - - - - - - * - - P b Q
On a horizontal line, mark points P and Q so that: PQ = b
At Q, erect a perpendicular QR so that: QR = a
Draw line segment PR.
. . Then: ./ RPQ = θ
lol, yeah XD, , u can't find this Question anywhere T^T. I see that we are very similar to each other lol. We both seek answers online INSTEAD OF working our asses off :P.
I was searching for assignment2Q5, and i landed on ur post and i found it SOO strange that ur Q was the same as my assignment and u posted it like the day it was released or something lol. Anyways, i was suspicions and now here I am searching for the same Question as u have right now and landed on ur post .
Can't seem to find Q1 (proof >_<, they discuss about it, but no proofs), and Q3 (don't understand), i found all other Qs or did them manually. ♥ internet ♥