For questions about triangles
1
vote
1answer
132 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 ...
0
votes
2answers
75 views
A question on Trigonometry (bisector)
If two bisector of a triangular is equal, then it is Isosceles triangular.
1
vote
2answers
70 views
Triangle $\Delta ABC$ , $a,b,c$ are in G.P.
If in a triangle $\Delta ABC$ the sides $a,b,c $ are in Geometric Progression.Find out the range of common ratio of the Geometric Progression.
I understood that the twist is that we are bound under ...
0
votes
0answers
40 views
Law sines in Spherical Triangle $\rightarrow$ Law sines in plane triangle
Could any one tell me how to estimate or get law of sines in Spherical Triangle to The Law of Sines in Plane Triangle? i.e $\frac{\sin a}{\sin A}=\frac{sin b}{\sin B}=\frac{\sin c}{\sin C}$ to ...
2
votes
1answer
148 views
Finding side and angle of isosceles triangle inside two circles
I'm having a problem that I'm not sure how to solve (or if it's even possible). It's not homework, just something i'm struggling with for a project. :)
Basically, there are two circles, represented ...
6
votes
2answers
106 views
Concurrency of A'L, B'M, C'N.
Need some help with the following problem.
Problem: In $\triangle ABC$ the midpoints of $BC$, $AC$, $AB$ are $L, M,$ and $N$ respectively, and the points on the circumcircle opposite to $A, B,$ and ...
1
vote
1answer
56 views
How to prove triangle inequality for given formula?
How to prove that given formula $\frac{(P-Q)^2}{P}+\frac{(P-Q)^2}{Q}$ satisfies triangle inequality ?
2
votes
1answer
58 views
Does the orthocenter have any special properties?
Each of the commonly known triangle centers I know has some sort of special property. For example:
The incenter is the center of the inscribed circle.
The circumcenter is the center of the circle ...
6
votes
2answers
128 views
Equilateral triangle geometric problem
I have an Equilateral triangle with unknown side $a$. The next thing I do is to make a random point inside the triangle $P$. The distance $|AP|=3$ cm, $|BP|=4$ cm, $|CP|=5$ cm.
It is the red ...
2
votes
4answers
135 views
Circle/Triangle math problem
The question asks to find angles $\angle X$ and $\angle Y$, however I don't know how to do this without assuming that lines $\overline {GO}$ and $\overline{OJ}$ are parallel. The only angle given is ...
3
votes
2answers
75 views
Solving for the triangle's perimeter
Would like some help with solving for the grey triangle's perimeter. It is assumed that the grey triangle is equilateral.
My attempt:
Let $x =$ side of grey triangle
Let $h =$ height of grey ...
5
votes
2answers
166 views
Problem with the Pythagorean theorem [duplicate]
The Pythagorean theorem has already been proved and it is a basic fact of math. It always works, and there are proofs of it. But I have found a problem.
Say you want to get from point ...
4
votes
1answer
74 views
Packing three squares into an equilateral triangle
I am trying to pack 3 equal, largest possible sized squares into an equilateral triangle.
1
vote
0answers
33 views
Two coloured plane
Can you prove that For any two angles $θ,ϕ$ there exists a monochromatic triangle that has angles $θ,ϕ,180−(θ+ϕ)$ in two coloured plane?
0
votes
1answer
298 views
Determine angles of triangle given nothing (no scientific calculator) but triangle sides.
The question says it all.
Given a triangle, find its angles without a calculator. Is this even possible without tables or making tables?
Summary:
Is it possible to determine the inverse sin, cos of ...
0
votes
0answers
64 views
Finding a formula for perimeter of triangles in triangle
I hope you are familiar with counting triangles in triangle problem. I've studied it a little recently. Now i want to find a formula for sum of perimeters of this all triangles but i don't know how to ...
1
vote
1answer
133 views
Existence of Gergonne point, without Ceva theorem
The intersection at one point (called Gergonne point) of the lines from vertices of a triangle to contact points of the inscribed circle can be proved immediately using Ceva's theorem.
Is there a ...
1
vote
3answers
152 views
Connecting midpoints of sides of a triangle
In triangle $\triangle ABC$, $AB=8$, $BC=14$ and $CA=10$. Points $M$, $N$, and $P $ are the midpoints of sides $AB$, $BC$, and $CA$, respectively. If $M$, $N$, and $P$ are connected to form a ...
1
vote
2answers
195 views
Finding the area of a triangle using fractions?
To find the area of the triangle do you use Pythagorean theorem from what you have? Could this use similar triangles.
0
votes
2answers
41 views
2
votes
1answer
119 views
Construct a Triangle from Given Base, Obtuse Angle Adjacent to Base and Difference of Two Other Sides
I need to construct a triangle from given base, obtuse angle adjacent to base and difference of two other sides.
Let us try to analyze the scenario.
We are given base BC, obtuse ...
7
votes
1answer
85 views
Geometric inequality with a triangle
The positive real numbers $x,y,z$ are the side lengths of a triangle iff $$x^2 + y^2 + z^2 < 2\sqrt{x^2y^2 + y^2z^2 + z^2x^2}$$
0
votes
1answer
60 views
How to determine a Triangle vertices by its coordinates?
I have to solve this problem, yet I'm not sure what is asked.
Given a triangle whose vertices are defined by its coordinates. Determine where is the point O with the given coordinates - inside or ...
5
votes
4answers
147 views
How to know location of a point?
I have a circle formed with three given points. How can i know whether another given point is inside the circle formed by previous three points. Is it determinant i need to calculate? Then what are ...
0
votes
2answers
305 views
Isosceles Triangle how to find the base?
Two sides of a triangle each have length of 5. All of the following could be the length of the third side Except.
A 1
B 3
C 4
D 7.07 or √50
E 10
Do I use the formula 2√L^2-A^2 in order to find ...
3
votes
2answers
171 views
2
votes
3answers
50 views
getting the inner corner angle
I have four points that make concave quad:
now I wanna get the inner angle of the (b) corner in degrees.
note: the inner angle is greater than 180 degree.
5
votes
3answers
82 views
What characteristic of the triangle leads the the existence of the orthocenter
We all know that all three altitudes of a triangle meets in the orthocenter of the triangle. It's a quite classical problem and is proven.
However, what I really wanna know is what characteristic of ...
2
votes
2answers
473 views
How to find surface normal of a triangle
If I have a triangle with $3$ points $P_1, P_2,$ and $P_3$, each with $x, y,$ and $z$ coordinates, how do I find the surface normal $N$ in $x, y,$ and $z$ such that
$$N_x+N_y+N_z = 1$$
I'm looking ...
1
vote
2answers
65 views
Question about Geometry involving angles and lines
The answer is C however if angle ACD is 110 degrees and angle AB is 110 degrees how does it equal 180?
1
vote
2answers
73 views
Help with basic trigonometry
it's been many years since I was at school and I never did algebra so I'm having a real hard time understanding trigonometry again.
ALL the sites just say use this easy formula to calculate it:
...
3
votes
1answer
86 views
Why does $b^2 = c^2 + a^2 - 2ca\cos(B)$ in trigonometry?
http://i.stack.imgur.com/l0Dw7.png
I have a (what I believe to be an isosceles) triangle and the formula $b^2 = c^2 + a^2 - 2ca \cos(B)$ and I just have to "prove it".
Now this really confused me as ...
1
vote
1answer
316 views
How do I find the angles of a triangle if I only have the lengths of the sides?
Is it possible to find the angles of a triangle if I only have its sides?
If so, how can I achieve this?
Regarding my knowledge of triangles:
Whilst I was taught trigonometry a few years ago, I ...
2
votes
3answers
214 views
Proof of Cauchy–Schwarz inequality
I was reading about the Cauchy–Schwarz inequality from Courant, Hilbert - Methods Of Mathematical Physics Vol 1 and I can not understand what they mean when they said the line that has been ...
0
votes
0answers
57 views
Sum of angles in a hyperbolic triangle with one ideal angle
I want to calculate the sum of the angles of the triangle formed in the hyperbolic plane from the points $(-1,1), (0,1)$, and $(1,1)$. This forms an angle at the origin which has an infinite slope for ...
2
votes
1answer
613 views
Calculating circle radius from two points on circumference (for game movement)
I'm designing a game where objects have to move along a series of waypoints. The object has a speed and a maximum turn rate. When moving between points p1 and p2 it will move in a circular curve ...
1
vote
1answer
137 views
How would I find the area of a triangle given three sides and using either the sine/cosine laws?
Triangle ABC has sides $8.5m$ (a), $7.1$ (b), and $9$ (c). I have been asked to find the area of the triangle using trigonometry.
2
votes
2answers
89 views
Solving for the length of a side of a triangle
I have a problem in which I'm supposed to solve for the length of the two sides of the triangle below. I assumed that it would simply boil down to $x+5=\sqrt{4x+52}$, and converted to standard form, ...
4
votes
2answers
226 views
Combinatorics. Inscribed Triangle in a decagon. No shared sides.
How many different triangles can be inscribed inside a regular decagon such that
the triangle shares its vertices with the vertices of the decagon, but the triangle shares none of its sides?
Here is ...
0
votes
1answer
32 views
10.5“ and 32” hypotenuse, a=8.5, b=42.5, what angles are the 10.5“ and 32” Hypotenuse?
I have a ramp that has a concave "kink" in the angle.
The first length of the hypotenuse is 10.5", the next is 32".
The triangle is 8.5" tall (a)
The triangle is 42.5" long (b)
How do I figure ...
3
votes
1answer
96 views
points inside square that form a triangle
the following question beat me. How from given any 9 points inside a square of side 1 we can always find 3 which form a triangle with area less than $1/8$ .
0
votes
0answers
55 views
Figuring out angles of a second triangle based off of one side of a first
My friend and I are developing some image tracking software for a robot we are creating and we have this right here:
...
2
votes
3answers
2k views
Given the base and angles of an isosceles triangle, how to find length of the two sides?
I can't seem to find a textbook solution to this. It is always assumed that the length of the sides is know.
Isolceles triangle
So the base $a$ is known. The bottom angles where $\alpha$ and the ...
-4
votes
2answers
141 views
As shown in the figure: Prove that $X=30.$
Any idea about this problem:
As shown in the figure: Prove that $X=30.$
4
votes
2answers
762 views
Can every triangle be divided into five isosceles triangles?
Moderator Note: this is a question from the Federal Mathematics Competition 2013.
That's my problem: Can every triangle be divided into five isosceles triangles?
I've got to give evidence why ...
44
votes
10answers
5k views
What's a proof that the angles of a triangle add up to 180°?
Back in grade school, I had a solution involving "folding the triangle" into a rectangle half the area, and seeing that all the angles met at a point.
However, now that I'm in university, I'm not ...
0
votes
2answers
155 views
3d geometry: triangle 2 points known, find 3rd point
I have a 3d triangle ABC. Lengths AB, BC, and AC are known. Coordinates of points A and B are known. Point C only the y value of the coordinate is known.
I believe there are 2 points that can satisfy ...
3
votes
1answer
91 views
High School Geometry - If $BC$ is the greatest side of $\triangle ABC$, $D$ & $E$ are points on $BC, CA$…
If $BC$ is the greatest side of $\triangle ABC$, and $D$ & $E$ are points on $BC$ & $CA$, respectively, prove that $BC \ge DE$.
Clearly, equality holds iff $D$ is on $B$ and $E$ is on ...
-3
votes
3answers
123 views
How do I show that the pythagoras theorem holds for the specific case of an “isosceles right triangle”?
Figure shows a rectangle $ABCD$ and an isosceles triangle $\triangle DEC$.
$AD=BC=z$;$AB=DC=y$;$DE=CE=x$
One solution is as follows.
We know that the pythagoras theorem holds for a right triangle ...
1
vote
1answer
471 views
Finding the line integral around a triangle
How can I determine $\int xy \;ds$ of a triangle with points $(0,0)$, $(1,0)$ and $(1,1)$
*The integral has the letter $C$, which I am not sure how to input here.
I know it may seem easy, but I am ...
