For questions about properties and applications of triangles

learn more… | top users | synonyms

6
votes
3answers
329 views

Why Doesn't This Integral $\int \frac{\sqrt{x^2 - 9}}{x^2} \ dx$ Work?

I am trying to solve this integral, which is incorrect compared to Wolfram|Alpha. Why doesn't my method work? Find $\int \frac{\sqrt{x^2 - 9}}{x^2} \ dx$ Side work: ...
0
votes
1answer
100 views

A question on triangles

The radii $r_1,r_2,r_3$ of ex-scribed circles of the triangle $ABC$ are in harmonic progression. If the area of the triangle is $24$ sq.cm and its perimeter is $24$ cm, then what is the length of the ...
1
vote
2answers
131 views

Triangle Requirements based of triangle Inequality

In a Geometry course we are dealing with triangle inequality and two statements arose: "For any triangle, any side is smaller the the sum of the others." and "For any triangle, the largest side is ...
0
votes
1answer
2k views

probability of three random points inside a circle forming a right angle triangle

three points are randomly chosen on a circle. what the probability that 1.triangle formed is right angled triangle. 2.triangle formed is acute angled triangle. 3.triangle formed is obtuse angled ...
4
votes
2answers
235 views

Does “triangle” in English exclude degenerate triangles?

Just for fun read few problems on the projeteuler.net website. Number 276 found interesting: Consider the triangles with integer sides a, b and c with a ≤ b ≤ c. An integer sided triangle ...
3
votes
1answer
236 views

Heronian triangles

How to prove that all Heronian triangles can be found using formulas described here? I understand that the described substitution will give Heronian triangle, but how to prove that using the ...
7
votes
3answers
289 views

Elementary Geometry

The side of the square measures $1\ \mathrm{cm}$ , and $AC = 1\ \mathrm{cm}$, find the value of $AB$
2
votes
3answers
234 views

Vector path length of a hypotenuse

Consider the red path from A that zigzags to B, which takes $n$ even steps of length $w$. The path length of the route $P_n$ will be equal to: $ P_n = P_x + P_y = \frac{n}{2}\times w + ...
3
votes
3answers
487 views

Heronian triangle Generator

I'm trouble shooting my code I wrote to generate all Heronian Triangles (triangle with integer sides and integer area). I'm using the following algorithm $$a=n(m^{2}+k^{2})$$ $$b=m(n^{2}+k^{2})$$ ...
3
votes
1answer
340 views

Is there a way to tessellate an area using triangles and minimize/specify the number of unique triangles?

Is it possible to tessellate a planar surface from triangles but with the following constraints: density (average number of triangles) can be varied. a finite set of unique triangles are used for ...
1
vote
2answers
1k views

Integrate using Trigonometric Substitutions

Evaluate the integral using trigonometric substitutions. $$\int{ x\over \sqrt{3-2x-x^2}} \,dx$$ I am familiar with using the right triangle diagram and theta, but I do not know which terms would ...
1
vote
0answers
453 views

General formula for computing triangular gaussian quadrature.

While this is a simple question, I'm totally lost. Is there any general formula for generation of n-point gaussian quadrature over a triangle? I'll use this formula to generate a variable-point (7, ...
3
votes
2answers
492 views

Sierpinksi like triangle construction. How to find the number of triangles in each iteration?

So here is the question: If we look at the Sierpinski triangle (left column of attached image) and think about how many triangle's it takes to make the shape at each iteration we can get the sequence ...
0
votes
1answer
2k views

Ordering vertices in counter-clockwise manner in 3D space.

This is my first question in math and if I cannot get it right for the first time, please forgive me. I'm working on a simulation and I need to order vertices of a triangle in counter-clockwise ...
0
votes
1answer
154 views

Euclidean Geometry a triangle problem

In the three dimensional figure below, is there a way to prove that $$ \angle MNK = 90^ \circ $$ $\hspace{2.8in}$
11
votes
1answer
1k views

The Ellipse Problem - finding an ellipse inside a triangle

The problem statement is as follows: A triangle is dissected into six smaller triangles by its angle bisectors. Prove that the intersections of the angle bisectors of each of these smaller triangles ...
3
votes
1answer
322 views

How do you split a 90-45-45 triangle into equal area strips?

How do I find the values for $a_0, a_1, \ldots, a_n$ such that the triangle is divided into $n+2$ parts of equal area? In the above example, $n=2$. Let's assume that $a_i = 0$ means the line is at ...
0
votes
2answers
307 views

Given triangle ABC, if D is an interior pt and E is an exterior pt, segment DE intersects triangle ABC?

This is regarding neutral geometry I think. It seems to be obviously true but I struggle to prove it. My 'proof' goes by the following: since $E\notin\mathrm{ int}(\triangle{ABC})$, there exist an ...
17
votes
1answer
66k views

Solving Triangles (finding missing sides/angles given 3 sides/angles)

What is a general procedure for "solving" a triangle—that is, for finding the unknown side lengths and angle measures given three side lengths and/or angle measures?
1
vote
1answer
112 views

Sum of heights from a random point in triangle?

I've used an easy lemma for a problem about heights from a random point $O$ inside a equilateral triangle. It's easy to prove that $OA'+OB'+OC'=h$, where $A'$, $B'$ and $C'$ ...
0
votes
4answers
4k views

Solving a triangle given two side lengths and the measure of a non-included angle

Let's say given an angle A = 46 °, side a = 2.29 and b = 2.71 I figured that the angle B = 58.4 by saying: $$B = \sin^{-1} \left(\frac{ 2.71 \sin{46^{\circ}}}{2.29}\right)=58.4^{\circ}$$ But I ...
0
votes
2answers
3k views

Solving a triangle, given two sides and the measure of the included angle

Let say you have a triangle Angle A = 41 degrees , side b = 3.41 and c = 5.83 can you use pythagoras theorem to find the side a? and how can you find Angle B and C
2
votes
1answer
387 views

Find angles using the Law of Cosines

if you must find the Angle C based on the sides of a = 2, 3 b = 4,6 og c = 5, 9  I have used the formula: $$\cos (C) =\frac{a^2 + b^2-c^2}{2ab}$$ use, but I think i'm doing something wrong: ...
0
votes
1answer
1k views

Solving triangles and quadratic equations

When calculating the pieces in a triangle with only two sides and an intermediate angle is known, one must solve a quadratic equation. By solving the equation are 2, 1 or 0 solutions, as ...
2
votes
1answer
169 views

Similar Right Triangles and Incircles [duplicate]

Possible Duplicate: Triangle and Incircle In a setup of right triangles ABC, BDA, and BDC not unlike this diagram (click on the link, and ignore the written side measures and subtext in ...
0
votes
1answer
161 views

30 60 90 Triangle question.

A right triangle has a hypotenuse of $\sqrt{10}$, one of the legs is $x+2$, and the shortest leg is $x$. How do I find $x$? Thanks.
2
votes
1answer
337 views

Sum of Angles in a Triangle.

Can anyone please explain how to form a better idea in understanding Sum of measures of angles in a triangle are 180 degrees.
0
votes
1answer
97 views

Finding a point which is constrained to 3 other points.

Is there an easy way to find the 4th point given 3 fixed points and a different minimum length between the 4th point and each of the 3 points? Similar to this question, but with non-fixed minimum ...
3
votes
1answer
379 views

Maximum triangle area

I have a small problem. Consider I have a triangle. Which maximum area can it cover if two of his medians are 3 and 8? I think I'll need to use derivative here, but firstly I need to find a function ...
0
votes
2answers
343 views

How do i find this angle in a right triangle?

So i'm writing a program, and i need to write a method that will give me the angle of a specific angle of a triangle when i know only the adjacent length and opposite length. I know that "tan(A) = ...
3
votes
1answer
178 views

Algebra question about Triangle Interiors

I was reading about Triangle Interiors on Wolfram Alpha: http://mathworld.wolfram.com/TriangleInterior.html and they have a simple equation: $$\mathbf{v} = \mathbf{v}_0 + a\mathbf{v}_1 + ...
0
votes
1answer
264 views

How do we derive the direction formula for longitude latitutude

θ = atan2( sin(Δlong).cos(lat2), cos(lat1).sin(lat2) − sin(lat1).cos(lat2).cos(Δlong) ) Does it take into account that we may be dealing with a trapezoid rather than a rectangle ...
7
votes
2answers
575 views

The incenter and Euler line.

It seems well known that the incenter of a triangle lies on the the Euler line if and only if the triangle is isosceles (or equilateral, but that is trivial). Searching the internet, I could not find ...
0
votes
0answers
202 views

Uniform Random Points on a triangle using only edge plane normals

For a triangle $ABC$ in 3D (each point has x, y, z coordinates) is it possible to generate uniform random points on the triangle from only the following data: Normal of the triangle plane $N = ...
2
votes
4answers
488 views

Proving $a^2+b^2=c^2$ where $a,b,c$ are side lengths of a right triangle.

Proving $a^2+b^2=c^2$ where $a,b,c$ are side lengths of a right triangle. First, I have never done a proof before, sorry I am so poor here. I have spent many hours but my actions have mostly used ...
2
votes
1answer
278 views

How to describe foсi of en ellipse inscribed in the triangle thru triangles angles points?

I was looking at Marden's theorem and could not help but wonder how foсi of en ellipse inscribed in the triangle can be described thru triangles angles points?
4
votes
2answers
259 views

Geometric inequality: $2r^2+8Rr \leq \frac{a^2+b^2+c^2}{2}$

Suppose $a$, $b$, and $c$ are the lengths of the sides of a triangle, and $R$ and $r$ are its circumradius and inradius respectively. How can one prove the following inequality? $$2r^2+8Rr \leq ...
6
votes
2answers
2k views

Is an equilateral triangle the same as an equiangular triangle, in any geometry?

I have heard of both equilateral triangles and equiangular triangles. (For example, this sporcle quiz lists both.) Are these always equivalent, regardless of geometry? I know they are the same in ...
3
votes
4answers
558 views

Simple trigonometry question (angles)

I am starting again with trigonometry just for fun and remember the old days. I was not bad at maths, but however I remember nothing about trigonometry... And I'm missing something in this simple ...
0
votes
3answers
779 views

general triangle angles and lengths

Pythagoras shows us how to find the 3rd side length on a right angled triangle where the two lengths connected by the 90 degrees are known. Additionally there is a surprisingly short equation that I ...
8
votes
2answers
708 views

Sangaku: Show line segment is perpendicular to diameter of container circle

"From a 1803 Sangaku found in Gumma Prefecture. The base of an isosceles triangle sits on a diameter of the large circle. This diameter also bisects the circle on the left, which is inscribed so that ...
1
vote
3answers
318 views

Systems of equations finding right triangles

I need help setting up the equation for the question, "Find all right triangles for which the perimeter is $24$ units and the area is $24$ square units." I know that the area is $A = \frac12 b h$ ...
0
votes
1answer
79 views

Quadratic Equation related question.

So here's the question : The hypotenuse of a right triangle is $3 \sqrt 5$ cm. If the smaller side is tripled & the larger side is doubled, the new hypotenuse will be $15$ cm. Find the length of ...
1
vote
3answers
223 views

Intuition around why Sine of X angle always equals same result.

My understanding so far. Sine represents a ratio of two sides of an interior angle within a right angle triangle. So given the three lengths of a triangle you can find the sine of any of the 3 ...
7
votes
4answers
481 views

Right triangle where the perimeter = area*k

I was doodling on some piece of paper a problem that sprung into my mind. After a few minutes of resultless tries, I advanced to try to solve the problem using computer based means. The problem ...
2
votes
2answers
324 views

Isosceles Trapezium problem

I came across a problem in a certain quiz which I couldn't solve. Here it is reproduced: Since $BX$ is midpoint of $AB$, $AB = CD = 2$ . Now $AD$ and $BC$ remain to be calculated. How can the right ...
0
votes
2answers
191 views

What is wrong with my algorithm (finding if the origin is within a triangle's interior)?

I am working on Project Euler Problem 102 and I thought I had a solution, but it seems I do not. Now, don't give me the solution. I know I'm on the right track. What I want to know is why my method ...
0
votes
1answer
600 views

Computing circumcenter of triangle in 2D with MATLAB

I'm writing a finite volume program over a 2D triangular mesh, and at one point I need to calculate the circumcenters of the triangles. The equation given in class and that on Wikipedia give different ...
30
votes
6answers
14k views

How many triangles are there?

The question is how many triangles are there in the following picture? I have thought to solve it by creating a formula based on the angles of the lines starting from the bottom of each side. I ...
-1
votes
2answers
8k views

Can we find the perimeter of a triangle given only its base and height?

How do you find the perimeter of a triangle that you only have the base and height measurements for? Please use ENGLISH and not difficult mathematical formulas! I understand little algebra so avoid ...