What is Triangle: Definition and 1000 Discussions

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted



△
A
B
C


{\displaystyle \triangle ABC}
.In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane (i.e. a two-dimensional Euclidean space). In other words, there is only one plane that contains that triangle, and every triangle is contained in some plane. If the entire geometry is only the Euclidean plane, there is only one plane and all triangles are contained in it; however, in higher-dimensional Euclidean spaces, this is no longer true. This article is about triangles in Euclidean geometry, and in particular, the Euclidean plane, except where otherwise noted.

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  1. D

    B What is the formula for calculating tributary areas in a slab on beam?

    I'm trying to derive these formulas of tributary areas of a slab on beam. The idea is simple.. portions of the rectangle is distributed to the edge by the formulas.. but inside a pure triangle area.. how do you compute for the 2 triangular areas and 2 trapezoidal areas?
  2. R

    MHB Answer to Student's Question on Right Angle Triangle

    A student ask me the question: Why the other angles in Right angle triangle can't be more than 90 degrees? I want to answer him correctly to the question, What Should I Say to Him?
  3. S

    Area of Triangle: Find the Unknown Formula

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  4. L

    MHB Find ∠A & ∠C in Triangle Geometry

    Let △ABC be a triangle. Let AD and CE be its internal bisectors, with D lying on BC and E lying on AB. Given that ∠CED=18° and ∠ADE=24°, how can I find angles ∠A and ∠C without aid of softwares? Angle ∠B is easy to calculate, as ∠CED+∠ADE=∠CAD+∠ACE=∠A+∠C2=180°−∠B2 42°=180°−∠B2 ∠B=96° The other...
  5. H

    MHB Triangle: calculate angle between raised height and angle follower

    One sharp corner of a right-angled triangle is 50º. Calculate the angle between the raised height and the angle follower at right angles. So I know that the angles are 90º, 50º and 40º. How do I find the angle between the raised height and angle follower?
  6. A

    MHB Drawing a pre-defined triangle that touches 3 pre-defined lines at all 3 points

    This is my first time posting here so please forgive me any indiscretions... I'm actually not a student. I'm a general contractor. Part of what I do for a living is draw plans, and that quite often involves geometrical and trigonometrical type challenges. For the most part, I'm usually able...
  7. A

    Which is harder to pull apart, a circle or a triangle?

    In deciding which shape of ring I should use to secure an anchor to an anchor trolley I came across two choices, a circular ring or a triangular ring. While either will surely work, I began to wonder which would be more difficult to pull apart. Most of the information I found is about forces...
  8. W

    MHB Find C's Coordinates for Right Triangle ABC

    Right triangle ABC. BC = a = sqrt(17) AC = b = sqrt(68) AB = c = sqrt(85) A's coordinates: 0,12 B's coordinates: 6,5 What's EASIEST way to get C's coordinates?
  9. binbagsss

    Triangle Inequality: use to prove convergence

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  10. opus

    Solving an oblique triangle. Looking for a correctness check

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  11. D

    MHB Length of sides of right triangle with 1 angle and 1 side

    Hello so I'm a high school student and I came up with this question and I wanted to know if this was possible to do? So I tried to research and find a way to find the length of DC and I couldn't find anything, so I am here to ask for help, is this possible? I figured it would go in the...
  12. lfdahl

    MHB A center of mass determined triangle: Find the angles of the triangle P_1P_2P_3

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  13. M

    MHB Find the $ACB$ Angle of Triangle ABC

    The triangle ABC is given. Find the $ACB$ angle if the orthocenter of this triangle belongs to the circumscribed circle of the triangle $AOB$, where O is the center of the circumscribed circle of the $ABC$ triangle.
  14. M

    MHB Prove Area of Equilateral Triangle

    In chapter 6, section 6.1 of David Cohen's Precalculus textbook Third Edition, page 368, I found an interesting geometry problem. Show that the area of an equilateral triangle of side s is given as shown in the picture. The hint given is this: Draw an altitude and use the Pythagorean...
  15. L

    Inner Product, Triangle and Cauchy Schwarz Inequalities

    Homework Statement Homework Equations I am not sure. I have not seen the triangle inequality for inner products, nor the Cauchy-Schwarz Inequality for the inner product. The only thing that my lecture notes and textbook show is the axioms for general inner products, the definition of norm...
  16. andrewkirk

    I Measuring Space Curvature w/ Swarzschild Coordinate System: Q&A

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  17. V

    Is the Left Angle of the CKM Unitarity Triangle Really Pi Minus Gamma?

    Homework Statement I want to proof for $$V_{us}V^{*}_{ub}+V_{cs}V^{*}_{cb}+V_{ts}V^{*}_{tb}=0$$ unitarity triangle that left angle is $$\pi-\gamma$$ (see below picture from my lecture notes). Homework Equations [/B] $$\gamma \approx - arg(V_{ub})$$ $$\beta_s \approx arg(V_{ts})+\pi$$...
  18. lfdahl

    MHB What is the Probability of Distances in an Equilateral Triangle?

    A point $P$ is chosen at random with respect to the uniform distribution in an equilateral triangle $T$. What is the probability that there is a point $Q$ in $T$ whose distance from $P$ is larger than the altitude of $T$?
  19. D

    Calculating magnetic induction in a triangle

    Homework Statement Three very long parallel conductors situated in the air make a direct-symmetrical 3-Phase system. The conductors pass through the A B C points of the triangle of side ##a##. The currents in the conductor form a direct-symmetrical 3-Phase system. Effective values of currents...
  20. alijan kk

    Triangle altitude's concurrency by symmetry

    Homework Statement in the proof of triangle altitudes concurrency , i have found the equation of the Altitude AD, x(x2-x3)+y(y2-y3)-x1(x2-x3)-y1(y2-y3) Homework EquationsThe Attempt at a Solution In the book other altitude equations are written by symmetry, how is the idea of symmetry is used...
  21. Y

    MHB Equilateral triangle within a circumscribed circle

    Dear all, In the attached picture there is an equilateral triangle within a circumscribed circle. MW is a radius of the circle, and I wish to prove that MT = TW, i.e., that the triangle cuts the radius into equal parts. I thought perhaps to draw lines AM and AW and to try and prove that I get...
  22. lfdahl

    MHB Equlateral Triangle: Prove $ab \cos \gamma = ac \cos \beta = bc \cos \alpha$

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  23. K

    Triangle inscribed in a circle

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  24. Y

    MHB The area of a triangle and determinants

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  25. B

    Second moment of area of a hollow triangle

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  26. T

    Solving for the third one should be straightforward.

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  27. wukunlin

    I Putting a point inside a triangle in 3D space

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  28. M

    MHB How can we parametrize the triangle?

    Hey! :o I want to calculate $\iint_{\Sigma}xdA$ on the triangle with vertices $(1,0,0)$, $(0,1,0)$ and $(0,0,1)$. We have to define the surface $\Sigma(u,v) = (x(u,v), y(u,v), z(u,v))$ then we get $$\iint_{\Sigma}fdA=\iint_Df(\Sigma(u,v))\|\frac{\partial{\Sigma}}{\partial{u}}(u,v)\times...
  29. Y

    MHB Distance between points in a triangle

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  30. M

    MHB Unique Area of Triangle Formula

    I think the following formula is so cool.
  31. M

    MHB Is there a formula for finding the perimeter of a triangle with known vertices?

    The vertices of triangle ABC are A(1, 1), B(9, 3), and C(3, 5). 1. Find the perimeter of triangle ABC. I must use the distance formula for points to find the individual lengths. I then must add all 3 lengths to find the perimeter. Correct? 2. Find the perimeter of the triangle that is formed...
  32. J

    Geometry: Solve for angles of a triangle w/line intersecting

    My mother's boyfriend's son who is in 6th grade asked me a question about the math they are learning. I thought it wouldn't be too bad but I cannot for the life of me figure it out. A solution would be greatly appreciated. 1. Homework Statement https://postimg.org/image/1tsa4v4t8r/ Homework...
  33. M

    MHB Solving Acute Triangle Angles Given $A,B,C$ & Equations

    Given that $A,B,C$ be angles in an acute triangle. If $(5+4\cos A)(5-4\cos B)=9$ and $(13-12\cos B)(13-12\cos C)=25$ find $cos(A+C)$. I know $A+B+C=180^{o}$ and $\cos B=-\cos(A+C)$ and what next?
  34. A

    Magnetic field of off center triangle - Biot Savart Law

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  35. M

    MHB Is this triangle an isosceles triangle?

    Use the distance formula to show that the triangle with the given vertices is an isosceles triangle. A(0, 2), B(7, 4), C(2, -5) I must use the distance formula to find AB, BC and AC. Two sides or lengths must be equal and one side different to be an isosceles triangle. Correct?
  36. karush

    MHB 12.4.9 - Area of a triangle given points in 3D space

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  37. Mr Davis 97

    Proving the Triangle Inequality: ##|a-b| < \epsilon##

    Homework Statement If ##\forall \epsilon > 0 ## it follows that ##|a-b| < \epsilon##, then ##a=b##. Homework EquationsThe Attempt at a Solution Proof by contraposition. Suppose that ##a \neq b##. We need to show that ##\exists \epsilon > 0## such that ##|a-b| \ge \epsilon##. Well, let...
  38. T

    Faraday's law -- circular loop with a triangle

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  39. Brendan Webb

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    Homework Statement Consider an equilateral triangle of side 15.6cm. A charge of +2.0μC is placed at one vertex and charges -4μC each are placed at the two. Determine the electric field at the centre of the triangle. Homework Equations E=kQ/r^2 The Attempt at a Solution I am hoping someone...
  40. lfdahl

    MHB Show that there are points Q,R on C such that the triangle PQR is equilateral.

    Let $C$ be a smooth closed curve (no corners) in the plane with a convex interior, and $P$ a given point on $C$. Show that there are points $Q,R$ on $C$ such that the triangle $PQR$ is equilateral.
  41. lfdahl

    MHB Integer-Sided Right Triangle: 2001 Leg Length & Minimum Other Leg Length

    The shorter leg of an integer-sided right triangle has length 2001. How short can the other leg be?
  42. karush

    MHB S4.13.t.71 Angles of triangle PQR

    232.q1.4a sketch the region of integration $\displaystyle\int_{-2}^{2}\int_{\sqrt{4y^2}}^{4-y^2} f(x,y)\,dx \,dy$ this is what i did with desmos don't know how to shade the integrated area if the it is even correct😎
  43. N

    Equation for the amplitude of a line sweeping across a triangle

    Homework Statement I have a triangle with top sides of 5 mm (base is then 5*sqrt(2)). The top triangle has a line cut through it, at a height of 5/sqrt(2)/2. I want to compute the amplitude as function of position as a line sweeps into the triangle that is cut off. Requirement is A(0) = 0 and...
  44. T

    Geometry: Finding a Side Length in Triangle Using Centroid

    The Problem is #16 in the attached picture. Essentially, I need to find the length of BC using information about congruency and the location of the centroid. I've been able to show a whole bunch of things, but nothing that gets me close to actually finding out the missing side length. I began...
  45. M

    MHB What is the perimeter of triangle ABC?

    The vertices of triangle ABC are A(1,1), B(9, 3) and C(3, 5). A. Find the perimeter of triangle ABC. B. Find the perimeter of the triangle that is formed by joining the midpoints of the three sides of triangle ABC. For part A, must I use the distance formula for points on the xy-plane 3...
  46. A

    Find the ratio of two line segments in a triangle

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  47. peroAlex

    B-Field on Axis of Equilateral Triangle

    Homework Statement I came across a pretty interesting question that asks for magnetic flux density (B-field) on the axis of the equilateral triangle. This axis is meant to be perpendicular to triangle's surface passing through its centroid. Assuming that a triangle has sides denoted ##a## and...
  48. M

    Forces of 3 charges in an equilateral triangle?

    1. The problem statement: in the first photo all variables and given/known data, Homework EquationsThe Attempt at a Solution : i wrote it all down in the second photo [/B]
  49. karush

    MHB S4.13.t.71 angles of triangle PQR

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  50. A

    I Can a 63mm Bore Pneumatic Ram handle the required weight at an angled position?

    Hey So I am still a beginner in Physics and work asked me today to calculate if a 63mm Bore Pneumatic Ram will do the required job. Anyway, so I know how to calculate the weight capacity the ram can handle if it is at a 90 deg angle however if the ram is on an angle then I am stuck. I need to...
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