For questions about triangles

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3
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1answer
332 views

How can I calculate the transformation between two 3D triangles?

I am given the $3$-D coordinates of two triangles. For example: for $\triangle ABC$, the coordinates are: $A=(0, 0, 0)$, $B= (3.37576, 0, 0)$, $C=(5.14131, -2.47202, 0)$ and for $\triangle ...
4
votes
1answer
242 views

Similar - perspective triangles implies corresponding sides are parallel?

In a general homothetic transformation, if two triangles have corresponding sides parallel then the lines joining respective vertices are concurrent at the homothetic center. I was wondering if the ...
4
votes
1answer
1k views

Finding the distance between two gears

I have the following problem: In my class, we did a majorly complicated method to figure this out but I think there is a better way to do this... Here is the exact problem: A belt fits snugly ...
0
votes
1answer
637 views

Get the relation between X and Y axes in triangle based on the degree between

I have a given degree (0 - 360), and based on it, I'd like to be able to calculate the length of X and Y axis of a triangle built on that angle , if the third side of that triangle is equal to 1. I ...
1
vote
1answer
612 views

How can I calculate the transformation of two 3D triangles?

Given two triangle I have the transformation (three rotation followed by three translation)of both the triangles. How can I calculate the transformation between two triangles? A numerical example will ...
0
votes
2answers
2k views

maths - find vertices when 1 vertex and center point is given in polygon

I want to know if there is any general formula to find out vertices (co-ordinates) of a polygon (3 or more equal sides) when following is given: ...
3
votes
1answer
233 views

Help with a geometry problem involving triangles

My geometry book doesn't explain things very well so..... yeah I'm pretty sure that this has a simple answer, but my geometry book words it pretty weird. If triangle RST is congruent to triangle ...
0
votes
3answers
297 views

Calculate the position of Y when position X, distance to Y and the Angle is known

I'm trying to solve this problem: On a regular x/y grid, I have a point A located at position 2,7 (X,Y). I have to place a second point (B) on the grid (somewhere to the right of point A), but I ...
2
votes
2answers
101 views

Calculate x and y coord where line touch

Hi I got a 10 cm long line, and it touches point 1,1 I need to calculate where it touches x and y. If I think of it like an triangle i get the following information. One side is 10 cm. You get ...
6
votes
2answers
4k views

Proof that the angle sum of a triangle is always greater than 180 degrees in elliptic geometry

I've scoured the internet and have found many proofs showing that in Euclidean geometry, the angle sum of a triangle is always 180 degrees. I've also found many proofs showing that in hyperbolic ...
1
vote
1answer
1k views

The formula for finding the steepest curve between a range of x/y coordinates

I know approx what point i want from below diagram by looking at it(red circle), and im pretty sure there is some smart formula that does what im looking for, but how does the formula look like? ...
1
vote
1answer
1k views

Triangle inequality for positive definite symmetric real matrix

Show that \begin{equation} \rho(\mathbf{x},\mathbf{y}) = \sqrt{\sum\limits_{i,j=1}^n a_{ij} (x_i-y_i)(x_j-y_j)}, \end{equation} with $a_{ij} = a_{ji}$, $\mathbf{x} = (x_1,\ldots \;, x_n)$ and ...
2
votes
1answer
1k views

Positioning three circles, all of them touching each other

There are three circles, all of them touching each other. The bottom two circles are laying on an imaginary floor, such that they touch the line g=-r as well. Given are all three radii, r1 (A), r2 ...
0
votes
2answers
191 views

How long is side $c$ in this right triangle if $a = b$?

A right angled triangle has side lengths labeled as so. A common geometric construction that shows three squares sitting upon the sides of a right triangle with lengths A, B, and C However unlike in ...
14
votes
3answers
731 views

The Notorious Triangle Problem

I was told this question by a friend, who said that their friend had thought about it on and off for six months without any luck. I have then had it for a while without any luck either. It is in the ...
9
votes
2answers
2k views

Finding an angle within an 80-80-20 isosceles triangle

The following is a geometry puzzle from a math school book. Even though it has been a long time since I finished school, I remember this puzzle quite well, and I don't have a nice solution to it. So ...
4
votes
3answers
3k views

Find the coordinates in an isosceles triangle

Given: $A = (0,0)$ $B = (0,-10)$ $AB = AC$ Using the angle between $AB$ and $AC$, how are the coordinates at C calculated?
3
votes
1answer
2k views

Are isosceles always and only similar to other isosceles?

In my geometry class last year I remember putting down the statement in a column proof "That all isosceles are always and only similar to other isosceles". I do not remember what I was trying to ...
6
votes
1answer
2k views

RHS Congruency test - What makes 90 degrees different?

RHS is a well known test for determining the congruency of triangles. It is easy enough to prove it works, simply use Pythagorus' theorem to reduce to SSS. I thought that it seems strange that this ...