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. G

    Centroid of non-right triangle

    Homework Statement See attachment Homework Equations The Attempt at a Solution If the y-coordinate of the center of mass is given by (1/A)*∫y dA, how come the solution uses bh/2 as the area? This triangle isn't right angled so that area formula should not hold. What am I missing?
  2. T

    3 Equal Charges in Equilateral Triangle - Find KE @ Inf

    Homework Statement Question is attached. I know there's a few ways to solve this, but I'm wondering specifically why my integral of F ds isn't working. Homework Equations F = k * q^2 / r^2 U = ∫ F ds cos 30 = √3/2 s= rcos30 The Attempt at a Solution U = 2 * cos 30 * k *...
  3. C

    Finding the area of a triangle on a graph

    Here is the question: http://i259.photobucket.com/albums/hh299/the-real-guitar-hero/Capture_zpsf2b9cd28.png part A = 3√5 b=y=2X+1 c=(0,1) D is where I am confused. Area of triangle = (base x height)/2 from working out, line 2 cuts the x-axis at -1/2. line 1 cuts the x at 7. the height is 3...
  4. Petrus

    MHB How Can You Calculate the Area of a Triangle in an Orthogonal Coordinate System?

    In an orthogonal cordinate system determine the area of the triangle with vertices in (-4,1), (1,4) and (-5,10) There is prob many way to solve it so go ahead with your method:) I made a hint for vector method. Hint
  5. Petrus

    MHB Max Area of Triangle: x & y Axes & e^{-5x} Tangents

    considering the set of triangles, whose sides are the x and y axes, and the tangents to the curve e^{-5x}, x>0 to estimate the maximum area of such a triangle can be. I have no progress, well I know area is \frac{x*y}{2}.
  6. A

    MHB How to find angles of a triangle

    We know that in triangle ABC angle A equals \alpha and side a=\frac{b+c}{2}. How to find angles B and C knowing that B\geqslant C? For which values of \alpha the problem has solutions? ps. a, b, c are only notations. answer. \frac{\pi-\alpha}{2}\pm\arccos(2\sin\frac{\alpha}{2})
  7. R

    Electric field at the center of an equilateral triangle

    Homework Statement See attached image Homework Equations 1/4πε*q/r The Attempt at a Solution I know that since the problem gives centimeters, there are initial changes to units to be made in the permittivity constant. This makes it 8.86x10^-9 N/nanoCoulombs and 100 mm. But...
  8. R

    Finding the z component of vectors that form a triangle?

    For the vectors in the figure, with a = 1.1 and b = 2.6, what are (a) the z component of a x b, (b) the z component of a x c, and (c) the z component of b x c? Everything I've tried to look up involves vectors that are in unit notation, etc. I just don't understand how to do it when all you...
  9. S

    Is the Center of Mass Also the Midpoint of a Triangle?

    I blieve the mid point in space of arbitrary triangle formed by points A,B,C is the point at which the line A -> midpoint(B,C) B -> midpoint (A,C) C ->midpoint (A,B) meet (i also think C is redundant, that where A to mid and B to mid cross is basically the mid point of the whole...
  10. anemone

    MHB Determine the ratio of two angles in a triangle.

    Let ABC be a triangle such that \frac{BC}{AB-BC}=\frac{AB+BC}{AC}. Determine the ratio \frac{\angle A}{\angle C}.
  11. B

    Coulomb's Law involving triangle

    Homework Statement There are three point masses. 1 is fixed in space with the 2nd point mass directly below it on the ground. The 3rd point mass is an unknown distance to the right of mass number 2. These 3 point masses for a rt triangle with point 2 at the 90 degree angle. The vertical...
  12. R

    Fourier transform of a triangle function

    Homework Statement Hello I'm learning Fourier transforms via the Stanford lecture series on Youtube. In the 6th lecture, the professor claims that the FT of a triangle function is the square of the sinc function. I'm trying to derive this, but I can't get my math to work out. Could someone...
  13. O

    What is the inverse triangle symbol represent?

    Homework Statement B=magnetic flux density . A is the vector potential of magnetic field. How to get the formula B=∇A Homework Equations http://en.wikipedia.org/wiki/Magnetic_moment The Attempt at a Solution B=magnetic flux density . A is the vector potential of magnetic field...
  14. P

    Volume of bounded region and equilateral triangle

    Homework Statement y=x^2 y=1 Find the volume of the bounded region using an equilateral triangle cross section Homework Equations c^2=a^2+b^2 The Attempt at a Solution I'm will solve it with respect to x 1st. 2∫((1-x^2)h)/2 dx from 0 to 1 base=2(1-x^2) (2-2x^2)^2=(1-x^2)^2+h^2 4-8 x^2+4...
  15. S

    Vectors. Triangle Angle between vector

    Homework Statement Consider the points A(1,2) B(-2,-1) and C(3,-2) on the Cartesian plane. 1. Find the length of the segments AB and BC 2. Find the angle of the triangle at the vertex B Homework Equations Cosθ=(AB*BC)/|AB| |BC| ? The Attempt at a Solution The length of the...
  16. L

    Integral of 1/(x^2 + 36)dx When and how to draw triangle?

    1. ∫1/(x2 + 36)dx 2. I started by trying a trig substitution. The normal form, "a2 + x2, x=(a)tan(θ)," I thought could be reversed here: x2 + 62 x = 6tan(θ) dx= 6sec2θdθ ∫1/[(6tanθ)2 + 36] = ∫1/[36(tan2θ + 1)]*6sec2θdθ = ∫1/[36sec2θ]*6sec2θdθ = ∫1/6dθ = (1/6)θ + C...
  17. A

    Is Sin^2(a) Equal to Sin^2(b) + Sin^2(c) Only in a Right Triangle at A?

    Homework Statement prove that sin^2(a)=sin^2(b)+sin^2(c) if and only if ABC is a right triangle in A i worked really hard on this one I'm really confused why i didn' get the answer Homework Equations The Attempt at a Solution a+b+c=pi tried turning everythng to cos 2x didn't helpi...
  18. D

    Length contraction problem of right angled triangle

    http://https://www.physicsforums.com/attachment.php?attachmentid=56297&stc=1&d=1362318192 problem:- The situation is shown in attachment. the right angled frame of rods (in stationary ) is moving at speed v perpendicular to its hypotenuse. according to length contraction the corresponding...
  19. N

    Solving a 1415-gon Triangle Problem with the Pigeonhole Principle

    Hello. I have an example for you. I'm curious how. Yesterday I was on the mathematical competition. One example I can not solve. I want to know how. Can you help me, please? Consider a convex polygon of 1415 sides, which circumference is 2001 cm. Prove that between its peaks, there are 3 such...
  20. Albert1

    MHB Proof of Triangle Inequality: a+b-c, b+c-a, c+a-b

    Let a, b, c be the lengths of the sides of a triangle. Prove that: $\sqrt{a+b-c}$+$\sqrt{b+c-a}$+$\sqrt{c+a-b}\leq\sqrt{a}+\sqrt{b}+\sqrt{c}$
  21. D

    Electrostatic Force of a Triangle

    Homework Statement Suppose that the magnitude of the net electrostatic force exerted on the point charge q2 in the figure is 0.65 N . (Figure 1) http://imgur.com/4lZliPq Find the distance D. q1 = 2.1 micro C q2 = 6.3 micro C q3 = -.89 micro C Homework Equations F = k |q1|...
  22. T

    Number of unique paths in Pascal's Triangle

    Homework Statement Let pascal(n,i) be the value of the ith element of the nth row of Pascal's triangle. Using induction show that the number of unique paths from entry {0,0} to entry {n,i} in Pascal's triangle is equal to pascal(n,i). The Attempt at a Solution The base case n=1 seems easy...
  23. V

    Complex triangle equality & Sin(ntheta)/Sin(theta)

    Homework Statement The first problem is as follows And the second one is Homework Equations For the first question, I do not really know what equations to use. I tried writing it out in the form Z1 = a + ib, Z2 = c + id, etc, but that got me nowhere. The second question has been...
  24. M

    Geometry: Triangle with a Circumscribed and Inscribed Circle

    Homework Statement What is the area of a right triangle whose inscribed circle has radius 3 and whose circumscribed circle has a radius 8? Homework Equations The diameter must be the hypotenuse of the circle The Attempt at a Solution The answer is 57, but I do not know the...
  25. B

    MHB Internal angle sum of triangle

    Problem: Let A, B, C be three non-collinear points. Let D, E, F be points on the respective interiors of segments BC, AC and AB. Let θ, φ and ψ be the measures of the respective angles ∠BFC, ∠CDA and ∠AEB. Prove IAS(ABC) < θ +φ + ψ < 540 - IAS(ABC).(IAS means internal angle sum). Now I am...
  26. D

    Electric Potential of a triangle?

    Find the electric potential at point P in the figure. http://i.imgur.com/8FNSoML.png V = kq / r So what I did was calculated the electric potential each force gives on the point P. Vp1 = (8.99e^9) (2.75e^-6) / .625 Vp2 = (8.99e^9)(-1.72e^6) / .625 Vp3 = (8.99e^9) (7.45e^6) /...
  27. P

    Triangle angles >180 embedded

    Is it possible that a triangle with angles totaling over 180 degrees could exist without being embedded in a 3rd dimension?
  28. L

    Finding Volume of Solid: Isosceles Right Triangle Cross-Sections

    Hi, I'm still practicing how to find volume. 1. My problem is this: "Find the volume of the solid described below: The base of the solid is the disk x^2 + y^2 ≤ 4. The cross-sections by planes perpendicular to the y-axis between y=-2 and y=2 are isosceles right triangles with one leg in the...
  29. S

    Formula for the n-th row of Pascal's Triangle

    Homework Statement Find a formula for the sum of the elements of the nth row of Pascal's Triangle Homework Equations C(n,r) = [C(n-1,r-1) + C(n-1,r)] C(n,0) = C(n,n) = 1 The Attempt at a Solution I started with the summation of the elements in the rows n \sum^{n}_{r=0} C(n,r)...
  30. I

    Can you triangulate a triangle? (also, odd sided polygons to represent surfaces)

    EDIT: My guess to the below question is that no you can't triangulate a triangle because a legitimate triangulation each edge can only be linked up to exactly two distinct faces, so if you just have one triangle, each edge would be linked up to one face (the face of the triangle) I'm really...
  31. I

    Understanding Quotient Spaces of Triangles

    Hello, I have been given a homework problem and I don't want any help on solving the problem, (I'm not even going to post the problem - I want to figure it out myself), I only want to understand what the problem is asking. (That's why I've posted in this section rather than the homework...
  32. L

    Word problem: Finding area of a growing triangle.

    Okay, I tried to draw a picture of the graph the word problem is talking about. This is a bad picture, but it was the best my computer could take! :/ 1. Les triangles dangereux is an 80-minute movie showing nothing but a slowly growing triangle. It got a strong reception at Cannes...
  33. T

    Maximise perimeter of triangle in a circle

    Hey guys, I hope someone can give me some pointers with this because it should be really easy but I am just not getting it! I want to show that for a triangle inscribedin a circle an equilateral traingle gives the maximal perimeter. I've tried a few things and just get bogged down in algebra...
  34. F

    Triangle with Fubini - Solving Integral Problem

    Hi, I should Show the following: D is subset of R^2 with the triangle (0,0),(1,0),(0,1). g is steady. Integral_D g(x+y) dL^2(x,y)=Integral_0^1 g(t)*t*dt my ansatz: Integral_0^1(Integral_0^(1-x) g(x+y) dy) dx With Substitution t=x+y Integral_0^1(Integral_x^1 g(t) dt) dx...
  35. MarkFL

    MHB Finding the area of a triangle formed by 3 points in the plane

    Suppose we have 3 points in the plane given by: $\displaystyle (x_1,y_1),\,(x_2,y_2),\,(x_3,y_3)$ and we wish to find the area of the triangle whose vertices are at these points. We may let the base b of the triangle be the line segment between the first two points, and the altitude h of the...
  36. M

    Finding length of 3 sides of a triangle

    Homework Statement hi i have a photo with some given information. I need to find the length of all three sides of that triangle and also the area of the triangle I have already found them but i get 2 different results Homework Equations I have used both cosinus and pythagoras...
  37. A

    Proving the Centroid of ABC Triangle

    Homework Statement let ABC be a triangle where I divides angle BAC(angle A) => BAI=IAC Prove that I is the centroid of (B,AC)and (C,AB) Homework Equations i think phitagors wil come in handy but don't know how to use it The Attempt at a Solution let ac = a and AB = b aIB+bIC=0 (vectors)...
  38. D

    Find the angle of a triangle and x coordinate

    I have this triangle and I know just the two sides indicated there. How can I find angle theta? I tried decomposing the triangle in two right triangles and using trigonometry find one side, but I can't figure how to do that using just the hypotenuse
  39. C

    Same Areas of Trapezoid within Triangle, why?

    Good day, while reading up on an elementary math study book, i have encountered that a proof is build upon the following (see attachment for the figure). Are the Areas CDE and BED really the same? I tried to calculate this from abstraction, not sure where I could have made a mistake.. g1 is the...
  40. R

    Electric Field Strength at Center of Triangle

    Homework Statement Three positive charges, A, B and C, of 3 × 10-6, 2 × 10-6, and 3 × 10-6 Coulombs respectively, are located at the corners of an equilateral triangle of side 0.2 meters. Find the magnitude in Newtons/Coulomb of the electric field at the center of the triangle...
  41. M

    Vectors how are a,b,c in a+b+c=0 a triangle

    a, b, and c are unit vectors and a+b+c=0. This is the first part of a question and the solution involves the fact that a, b, and c form a triangle. I am having a really hard time how these vectors form a triangle. Can you pleases be as thorough as possible in your answer. Thank you so much for...
  42. A

    Finding the Normal Vector for a Triangle in the Plane Using Stoke's Theorem

    Homework Statement Let C be the oriented triangle lying in the plane 2x+y+z=4. Evaluate ∫ _{C} F*dr where F(x,y,z)=y2i + z - xk. Homework Equations I will be using ∫C∫curl F \bullet \vec{n} to solve this problem. But when I'm trying to find \vec{n} using -gxi - gyj + k, I get Using...
  43. R

    Triangle Area Calculation: Base 2 & 3/4, Height 4/9 | 11/18 Solution

    Homework Statement area of triangle with a base of: 2 & 3/4 and a height of 4/9 Homework Equations 1/2 * (b*h) The Attempt at a Solution i used: 1/2*(11/4 * 4/9) = 44/72 = 22/36 = 11/18
  44. C

    Pascals Triangle - Number of Routes on a Grid

    Homework Statement Deepa’s house is five blocks west and four blocks south of a bus stop. A store is three blocks west and one block south of the bus stop. How many ways can Deepa walk home if she wishes to stop on her way home by walking only west and south? Homework Equations...
  45. C

    Pascals Triangle (Checkerboard Question)

    Hello, I'm a little confused as to how I can go about solving this problem.. Any help is appreciated. Homework Statement Draw and copy the following checkerboard. Then, on the board, show all of the paths that the checker piece can take to reach the bottom square marked with an “X,”...
  46. G

    A function for a line in a square (or a triangle or a etc)

    a function for a line in a square (or a triangle or a pentagon etc) I don't have one off the top of my head (my maths is very rusty) but I think that ,starting from a cartesian point it is possible to create a function that allows one to draw a polygon in 2 or 3(?) dimensions. This...
  47. K

    Prove that the rᵗʰ term in the nᵗʰ row of Pascal's triangle is nCr.

    Prove that the rᵗʰ term in the nᵗʰ row of Pascal's triangle is nCr. nCr formula: n!/r!(n-r)! I've tried everything I can but I don't know how to approach this question.
  48. B

    MHB Show Cos A = 1/12 in Square ABCD

    In square ABCD need to show $cos a = \frac{1}{12}$
  49. U

    Need hlep with a triangle question (Trigonometry)

    I'm doing some trigonometry, and right now I'm given this equilateral triangle, http://i.imgur.com/WOPCk.png So how would I go about to find side AP, AQ, and PQ? I think I have a grasp of what it is, but not sure how to execute. I know you have 60 degree angle for ABC and all sides are 3, but...
  50. S

    Using the generalized triangle inequality

    Homework Statement Using the generalized triangle inequality, prove |d(x,y) - d(z,w)| ≤ d(x,z) + d(y,w) Homework Equations d(x,y) is a metric triangle inequality: d(x,y) ≤ d(x,z) + d(z,y) The Attempt at a Solution I know that this needs to be proved with cases: a) d(x,y) - d(z,w)...
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