For questions about properties and applications of triangles

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Fastest way to check whether the triangle inequality is satisfied

If we are given the lengths of the three sides of a triangle, and we simply add the 2 smallest sides and check to see if the sum is larger than the third side, will this always yield the correct ...
5
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3answers
430 views

Prime Number in triangle

I had a question here, the measures of the sides of a right triangle (a single unit) can be prime numbers? If they can not, why?! But, if you can, could you help me find an example?
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1answer
177 views

the ratio of the following two areas

Suppose you have the following triangle $ABC$: with the following properties: $|AB|=4\cdot |AA'|$, $|AC|=4\cdot |CC'|$, $|BC|=4\cdot |BB'|$. I have to find the ratio of the total area of the triangle ...
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2answers
130 views

Find The range of $r/R$.

Given a triangle $ABC$ with angle $A=90^{\circ}$. Let $M$ be the midpoint of $BC$. If the inradii of the triangles $ABM$ and $ACM$ are $r$ and$\ R$ respectively, then find the range of $\dfrac rR$ .
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4answers
119 views

How to mathematically define “on the outer side of the triangle”?

Given the coordinates of a triangle's vertexes, I'm trying to find its Fermat point programmatically. In one step of the algorithm that I'm trying to implement, I have to draw equilateral triangles on ...
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0answers
289 views

How to calculate Fermat point in a triangle most efficiently?

I am aware of this question, but mine is a bit more specific. I want to find the coordinates of the Fermat point for a given triangle. Assuming that no angle in the triangle is larger than 120 ...
4
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1answer
207 views

Could someone explain this animated gif to me in mathematical terms?

I understand that the area of the two squares around the right triangle are the total area of the one that is the hypotenuse. Is this just a proof for the Pythagorean theorem or is there some other ...
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1answer
220 views

A problem on triangle and its perpendicular bisectors.

I'm trying to solve the following problem : "In △ABC, coordinates of $B$ are $(−3, 3)$. Equation of the perpendicular bisector of side $AB$ is $2x + y − 7 = 0$. Equation of the perpendicular ...
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2answers
79 views

Sides from angles of a triangle

How does one find the side lengths of a right triangle in relation to each other using just the angles? I have all three angles. Is this even possible?
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1answer
385 views

find the rate of change of the area of triangle pulled by three people from its sides

this is the problem of my curious mind(I am it's designer!) . three people each having the rope attached by the end of the 3 sides of triangle ABC , pull the triangle with speed U in the direction ...
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3answers
67 views

Ratio of side length of triangle?

In triangle ABC, we choose a point D at AB such that the length of AD=1/2 AB, and point E at AC such that AE=3EC. F is intersection point of CD and BE. What is the ratio of CF/FD and BF/FE?
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1answer
804 views

Calculate Triangle Ground using Height and Top Angle

Is it possible to calculate the ground of a triangle only using the height and top angle. Click here to see a poorly draw sketch of what I'm trying to calculate. So is it possible and how, to ...
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4answers
210 views

equilateral triangle; $3(a^4 + b^4 + c^4 + d^4) = (a^2 + b^2 + c^2 + d^2)^2.$

In equilateral triangle ABC of side length d, if P is an internal point with PA = a, PB = b, and PC = c, the following pleasingly symmetrical relationship holds: $3(a^4 + b^4 + c^4 + d^4) = (a^2 + b^2 ...
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2answers
60 views

Is the orthocenter and incenter of a triangle the same point?

Although the orthoceneter and the incenter of a triangle are technically different things: The point in which the three altitudes of a triangle meet is called the orthocenter of the triangle. ...
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1answer
21 views

How do I find out the coordinates, interpolating across an angled line?

Suppose I know the coordinates of $A$ and $B$. The angle $X$ does not mean the total angle between the red lines, but rather how far along the angle that the purple line is. What is the easiest way ...
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1answer
86 views

portion of areas of two triangle

let us consider following picture we are given that this two line is parallel and also $AC=1/3 * AD$,we should find portion of areas of $ABC$ and $BCD$,now because $AB$ is one third of $AD$, ...
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1answer
569 views

A Question related to triangle and centroid .

The following is a geometry question I can't seem to get. "Consider an acute angle △ABC. Points D, E, F are mid points of sides BC, CA and AB respectively. G is the centroid of △ABC. Area of △AFG = ...
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2answers
113 views

Pythagoras Theorem in Triangles

The question is: In a triangle $\triangle ABC$, angle $\angle B = 90^\circ$ and $M$ is the mid-point of $BC$. Prove that $|AC|^2 = |AM|^2 + 3|BM|^2$. Please help me. I have tried various ways ...
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1answer
815 views

Find coordinates of vertex in right triangle

I have a right triangle with known points $A(x_1,y_1), B(x_2,y_2)$ and known cathetus $AC$ and $BA$. I need to find the coordinates of point $C$.
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3answers
661 views

Compare the sum of the squares of the median of a triangle to the sum of the squares of sides

You have to compare the sum of the squares of the median of a triangle to the sum of the squares of sides?
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1answer
216 views

Get legs length from right angle and hypotenuse

Here I have a 2 points. $A$ (lat,lng) and $B$ (lat,lng), this two point is hypotenuse of right triangle. How I can get legs length if I know angle, hypotenuse and these points?
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3answers
82 views

Sides of isosceles triangle

I have an isosceles triangle; the vertex angle and the base length are known (I think the base angles can be figured from this). How do I calculate the leg length?
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2answers
201 views

Calculating position/distance of point on arc of circle

I'm having a hard time trying to wrap my head around this problem. Imagine a line of length $A+B$ with center $C$, with a circle with $d = A+B$ with center at $C$. Now imagine drawing a line at ...
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2answers
86 views

Geometry Problem with isobarycenter and isoceles triangle

$XYZ$ a triangle with $XY=YZ.$ $D$ middle of $XY,$ $G$ isobarycenter of $XYZ.$ a circle $O,$ with center $D, XY$ are on $O.$ a circle $O',$ with center $G,$ $X$ and $Z$ are on $O'.$ 1/the ...
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1answer
190 views

What is the relation among sides of triangle in oval (ellipse)

if longest side of triangle is the longest diameter of oval, the rest point is located on the side of oval, you can vary it to change the triangle and except the longest side, set one of side of ...
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3answers
32 views

triangle row count from total points $x = \frac{n(n + 1)}2$

I'm trying to find the row count for triangle inputting the total number of points. I've found this, where $x$ is the total points, and $n$ is the rows. I'm having trouble solving it for $n$ $x = ...
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1answer
99 views

Help reducing the following expression involving Heron's formula for the area of a triangle.

Let $(ABC) = \sqrt{s \cdot (s - a) \cdot (s - b) \cdot (s - c).} $ This is Heron's formula for $(ABC),$ the area of $\Delta ABC,$ with sides $a, b, c,$ using $s = \frac{a + b + c}{2},$ the ...
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1answer
128 views

Triangle inequality for an obtuse triangle

$\alpha < 45^\circ$, how to show that 1) $|AB+AC|>|DB+DC|$? 2) $|AB+AC|>|DB+DC+DA|$?
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14answers
5k views

Do two right triangles with the same long hypotenuse have the same area?

I watched computer monitors and I asked myself, do two monitors with the same display diagonal have the same display area? I managed to find out that the answer is yes, if two right triangles with ...
0
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1answer
64 views

Use of triangle inequality for 2 triangles

In what angles of $\hat a, \hat b, \hat c, \hat d$ below conditions hold 1) $|AC+AD|>|BC+BD|$ or 1) $|AC+AD|<|BC+BD|$
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2answers
126 views

Calculate angle in triangle having 2 points and two lines

I have 2 points $B$ and $P$ and need to calculate angle $\alpha$ (maybe also I will need point $C$ and $E$) How can I do this. I know that I can calculate point $D$ it's $(\frac{1}{2}(x_P-x_B), ...
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3answers
356 views

How to be good at angles and trigonometry

I am Computer Science Engineer and loved algebra side of Mathematics. But when it comes to trigonometry and angles and triangles, I do not understand anything since college time. And till now also ...
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2answers
232 views

Properties of Triangle - Trigo Problem : In $\triangle $ABC prove that $a\cos(C+\theta) +c\cos(A-\theta) = b\cos\theta$

Problem : In $\triangle $ABC prove that $a\cos(C+\theta) +\cos(A-\theta) = b\cos\theta$ My approach : Using $\cos(A+B) =\cos A\cos B -\sin A\sin B and \cos(A-B) = \cos A\cos B +\sin A\sin B$, we ...
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1answer
57 views

Triangle of Multinomial Coefficients

What is the "Triangle Of Multinomial Coefficients" seen here: http://oeis.org/A036038 (OEIS: A036038) I can see that the diagonals of this triangle are just factorials... for example the last number ...
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2answers
702 views

word problem about right-angle triangle

An observer who is standing $47$ m from a building, measures the angle of elevation of the top of the building as $17°.$ If the observers eye is $167$ cm from the ground, what is the height of the ...
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2answers
103 views

Fitting circle into an angle

I've been struggling with this for quite some time now, anyone could help me perhaps with this? Given an angle of an arbitrary degrees, and a circle with radius r. And imagine I would try to push the ...
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3answers
133 views

Nature of a triangle with vertices $z_1, z_2$ and $-1$ such that $|z_1|=|z_2|=1=z_1+z_2$ [closed]

If $z_1$ and $z_2$ are distinct complex number such that $|z_1|=|z_2|=1$ and $z_1+z_2=1$, then the triangle in the complex plane with $z_1,z_2$ and $-1$ as vertices must be: equilateral. right ...
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1answer
130 views

Altitudes Ratio

If h, h', h'' denote the lengths of the three altitudes of a triangle, which of the following ratios never occurs as the ratio h: h': h''? ...
2
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1answer
70 views

find parameter for maximize area

suppose that we have Cartesian coordinate system.and suppose that we have three point which depend on parameter $t$,where t belongs to $(0,1)$;points are $A(cos(3-t),sin(3-t))$ $B(cos(t),sin(t))$ ...
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2answers
84 views

find angle in triangle

Let us consider problem number 21 in the following link http://www.naec.ge/images/doc/EXAMS/math_2013_ver_1_web.pdf It is from georgian national exam, it is written (ამოცანა 21), where word ...
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4answers
157 views

Where does $\sin 3° =3\sin 1° -4 \sin^3 1°$ come from?

Wikipedia makes the claim: "Though a complex task, the analytical expression of $\sin 1°$ can be obtained by analytically solving the cubic equation $\sin 3° =3\sin 1° -4 \sin^3 1°$ from whose ...
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2answers
222 views

$x \sin x=2$ why is my proof that there no solutions wrong?

$\frac 12 x \sin x=1$ . Let's look at a right triangle with base $x$ and altitude $\sin x$ . Then our equation is for the area of this triangle. Let the sides of the triangle be $a=x$ , $b=\sqrt ...
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1answer
44 views

Modification of the triangle inequality

We know from the triangle inequality that $X+Y \geq Z$, My question is under what conditions of $a,b,c$ (acute, obtuse or right angle) that $Z >X $ and $Z \geq Y $
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1answer
400 views

Move Point A along a line

Sorry, can't post images if my rep is below 10, and can't post more than 2 links. I removed the http section so it won't count as a link. I hope this isn't against forum rules, I'm not hurting anyone. ...
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2answers
256 views

Split a triangle into two right triangles

Lets assume I have a triangle $(p0, p1, p2)$ with $(p1 - p0)$ the longest edge. I am looking to find the point $q$ on the edge $(p1 - p0)$ such that $dot(p2 - q, p1 - p0) = 0$. That is to say; the ...
0
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1answer
72 views

Get Normal of a 3D point.

I have set of points. I created strip triangles using these points. Now I need to calculate normal. What I thought that for each triangle there should be a normal. But function I am using says that ...
3
votes
4answers
79 views

Limit on the expression containing sides of a triangle

To find the bounds of the expression $\frac{(a+b+c)^2}{ab+bc+ca}$, when a ,b, c are the sides of the triangle. I could disintegrate the given expression as $$\dfrac{a^2+b^2+c^2}{ab+bc+ca} + 2$$ and ...
0
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5answers
80 views

How to I find the length of a side on a triangle?

how do I find line AB in this if ac is 6cm, and bc is 14cm? angle A is 59*, c is 55*, and C is 66*. (not to scale) thanks in advance
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1answer
2k views

What's the ratio of triangles made by diagonals of a trapezoid/trapezium?

In the above image, what will be the ratio of areas of triangle $A$ and $B$? From Googling, I've found that: $\operatorname{Ar}(A) = \dfrac{a^2h}{2(a+b)}$ and $\operatorname{Ar}(B) = ...
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1answer
73 views

Radius of in-circle as a function of the center

I am trying to find the radius of an in-circle in a random triangle as a function of the center of the circle. Let (x,y) in\R^2 be the center of a circle, r the radius then i need an expression of the ...