For questions about triangles
3
votes
3answers
85 views
Maximum surface inside a triangle
If I have a triangle with sides of length a, b, c and I have a rope of length L,
what is the maximum surface of a boundary I can form with that rope that is entirely
inside the triangle.
Normally, ...
2
votes
1answer
42 views
Getting an acute angle for an obtuse angle using law of Sines.
I have done this problem over and over again. I even looked up tutorials on how to properly use law of sines. It's rather embarrassing that I'm struggling so much wish this simple trigonometric stuff.
...
4
votes
4answers
137 views
Is every prime number the leg of exactly one right triangle with integer sides? What's wrong with my argument that this is impossible?
The problem is: "prove that every prime number is the leg of exactly one right triangle with integer sides." However, I seem to have proved that this is impossible. What did I do wrong here?
Let ...
2
votes
2answers
24 views
Congruent Triangles
Triangle ABC and Triangle DBC are two isosceles triangles on the same base BC and vertices A and D are on the same side of BC.If AD is extended to intersect BC at P,show that
(a)Triangle ABD ≈ ...
1
vote
1answer
18 views
Sum of medians of a triangle
I'm very confused because I don't know how I can prove that the sum of the medians of a triangle is equal to the vector zero. Can someone give me a tip or something? Thanks! (And sorry if this ...
0
votes
0answers
28 views
Gergonne Point of a triangle coinciding with other triangle centers
I am trying to prove the following:
Let $T$ be the Gergonne point (the intersection of the lines that connect the points of tangency of the incircle with the vertices of the triangle) of $\triangle ...
1
vote
1answer
44 views
Is there an exploitable relationship between the angles of AB and AC in a triangle when moving point A?
I'm writing software to dynamically create a random, generated world (civ-esque), populate it with settlements, and draw roads between them. It would be relatively easy to draw roads like this:
...
4
votes
2answers
47 views
Coordinates of parallel triangle with a distance of 'd' between the parallel edges?
I have a triangle with Co-ordinates $\{(x_1,y_1),(x_2,y_2),(x_3,y_3)\}$. I need to find co-ordinates of a triangle,whose edges are exactly $\alpha$ distance from previous triangle. Below is the figure ...
1
vote
4answers
80 views
Triangle proof using law of sines
In triangle $ABC$, suppose that angle $C$ is twice angle $A$. Use the law of sines to show that $ab= c^2 - a^2$.
1
vote
1answer
50 views
arithmetic progression of triangle sides
Let $gcd(a,b,c)=1$ such that $a^2, b^2, c^2$ are in arithmetic progression. Show they can be written in the form
$a=-p^2+2pq+q^2$
$b=p^2+q^2$
$c=p^2+2pq-q^2$
for relatively prime integers $p,q$ of ...
1
vote
2answers
45 views
How to find co ordinates of a triangle after increasing the area by a factor of $\alpha$?
i am given with a triangle $\{(x_1,y_1),(x_2,y_2),(x_3,y_3)\}$ and the area need to be increased by a factor $\alpha$. can i anyone let me know formula to find the co ordinates of new triangle? There ...
0
votes
1answer
31 views
Triangle $z$-index interpolation between the vertices
I got a $2$D triangle, each vertex has a $2$D coordinate with a $z$-index value (NOT a $z$ coordinate!). The $z$-index value indicates whether a vertex lays on, in front of, or behind your screen ...
1
vote
1answer
102 views
Geometry - optimal 2D mesh between X expendable points
Say you have X points on a plane.
If you connect two points, you form a line. Connecting three points forms a triangle.
A line cannot cross a line, and a smaller triangle cannot be created inside a ...
-1
votes
0answers
37 views
Half angles and $\varphi$ [closed]
Anyone else notice $\varphi$ is also a half angle? If you look at the construction of the golden rectangle carefully, it uses ${\frac {x}{1+\sqrt {1+{x}^{2}}}}$ where $x$ is $2$ for $\varphi$. It is ...
0
votes
2answers
50 views
A question on Trigonometry (bisector)
If two bisector of a triangular is equal, then it is Isosceles triangular.
