I apologize in advance since I am not a native English speaker and thus I am not sure if I use the correct English terms for my question…
I know that 2 lines are "over" the sides of a triangle ABC
I know that both lines are 85cm each
I know that one line is on side A the other on side B
I know that both lines form an angle (or touch the ends) of side C
I know that angle C is 160 degrees
I know that both angles A and B are 10 degrees each
I dont know the length of C
I dont know the lenth of A and B sides
I know that A> 85cm, B>85 and that A=B
How could I calculate the lentgth of A and B?
Or if I cant what is the MINIMUM of extra data I need to be able to calculate the length of side A and side B? (and how) I cant stress the "minimum" enough 😛 I mean the worst case scenario what should I atleast know more not the best case scenario having plenty of data at my disposal 😛
I thought of extending the lines using the fact that they form an angle of 10 degrees with line C and find at which point those extended lines will intersect but I dont know the length of line C so I am stuck:P
Here is a drawing of the triangle for reference:
EDIT: @Brian Tung Well I would like to make a clarification for an insignificant detail there is no $x_2 , y_2$ its $x$ and $y$, the "thingy" next to them is supposed to be a question mark "?" (for everybody else I am referring to the triangle I draw in the OP) so its like $x$? $y$? (I thought that using the questionmark would denote that we dont know the values of $x$ and $y$ ) but I dont blame you for not being able to tell.. its a very bad drawing 😛
I hoped that I wouldn't need to come into this but it seems necessary 😛 This whole problem came up in a social network, it was a discussion about using certain machines in tight places were a girl expressed her opinion and a jerk ragetrolled her by saying that "spreading your legs there doesn't seem to be a problem" were the girl answered that spreading her legs obviously wouldnt be a problem since the size of her legs is 85cm so even if she tried a spagato at 178 degrees (her personal best 😛 ) the spread of her legs would be about 147cm since she would form a triangle were both sides would be 85 cm their angle would be 175 degrees and the spread she is looking for is the base of said triangle so the following would apply: $c^2=A^2 + B^2 – 2AB\cdot cos175$ (1)
But I know that its not true (And in my question changed the 178 degrees with 160 be able to make an easier picture for you guys not that it matters a lot but still :P)
And its not true because the base of her legs or else her (or if you like the neck of her femurs) dont attach and thus cant be the tip of the above mentioned theoretical triangle they have a distance between each other (distance which user "Brian Tung" labeled as "$z_2$" in his post) so (1) doesn't apply at least not with the given values since the tip of that triangle is further above (were the two $x$s in my drawing collide) thus the spread is bigger than 147cm…
But I dont know how to calculate that and I need to do so to post it to her and impress her 😀 obviously I could calculate the spread if I could measure previously mentioned distance $z_2$ but that would defeat the purpose… since if you can use a ruler to measure the distance between the her femur bone necks then why instead dont use a ruler to measure her leg spread to begin with?
But I guess if there isnt any other way to calculate said spread and make it look more "sciency" than just measure a value and apply basic arithmetic then I assume there are some standard bonesize ratios I could look up in order to claim for example that an adult woman with a leg of "85cm" has a pubis about "that big" thus the distance of her femur necks should be "that" long (= $z_2$) and by knowing that Ill follow $x=\left(\frac{z_2}{2}\right)\cdot cosign(10)$ (10 in case of my drawing were angles A and B are 10 degrees each) and applying the value ox $x$ to (1) finding the spread
But I hopes some of you guys could find a more elegant solution that wouldnt involve the value of $z_2$ 🙂
Best Answer
There are lots of different measurements that, if made, would permit you to determine the lengths indicated by $x_2$ and $y_2$ in the figure in question. For instance, if you knew $x_2$ itself, that would allow you to determine the distance $y_2$, and also vice versa, since
$$ \frac{y_2}{2} = (85+x_2) \cos 10 $$
However, I suspect that if you could easily determine either $x_2$ or $y_2$ themselves, you wouldn't be asking this question. A lot depends on what you can easily determine. One possibility is the distance between the ends of the $85$ cm lines. Call that distance $z_2$. In that case,
$$ y_2 = 170 \cos 10 + z_2 $$
and
$$ x_2 = \frac{z_2}{2 \cos 10} $$
For additional help, you'd have to tell us what you can easily determine.