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. V

    Equilibrium and principle of triangle of forces

    1. Homework Statement A rope of 5m is fastened to two hooks 4m apart on a horizontal ceiling. To the rope is attached 10kg mass so that the segment of the rope are 3m and 2m.Compute the tension in the string 2. Homework Equations Sine rule, cosine rule 3. The Attempt at a Solution...
  2. F

    Calculating Probability of 2 Black Balls from 3-Ball Urn w/ Pascal Triangle

    if we toss 4 coins and we want to know the probability of having 3 heads we can easily calculate that using pascal triangle . I want to know if we have an Urn that contain 3 balls : 1 black , 1 red, 1 yellow. and we want to draw 3 balls , but when we draw the first ball we put it back in the...
  3. V

    Principle of triangle of forces

    Homework Statement A body of mass 700g hangs from the end of a long wire fixed to a high tree. A horizontal string attached to the body pulls it until the wire is at 30 degrees to the vertical.Find the tensions in the both the string and the wire Homework Equations Sine rule The...
  4. H

    Triangle Inequality for integrals proof

    Homework Statement What I want to show is this: ∫|x+y| ≤ ∫|x| + ∫|y| Homework Equations |x+y| ≤ |x| + |y| The Attempt at a Solution So I thought if I used the triangle inequality I could get to something along the lines of: Lets g belong to the real numbers ∫|x+y| =...
  5. P

    Ceq of 3 capacitors in a triangle

    I'm a little confused about this problem. I attached the pic. The solution manual states " capacitors C1 and C3 are in series with each other and in parallel with capacitor C2." I don't understand why it has to be C1 and C3 in series which is parallel with C2. Can't it also be C2&C3 in...
  6. O

    Triangle tangent to circle problem using derivatives

    Homework Statement A metal bar of length l in the figure below has one end attached at a point P to a circle ofradius a < l. Point Q at the other end can slide back and forth along the x–axis. (a) Find x as a function of θ (θ=angle POQ). (b) Assume the lengths are in centimeters and the...
  7. M

    Find the height of any triangle?

    Homework Statement I have the side lengths of a triangle. The base is 190 ft long, side A is 182 ft long and side B is 363 ft long. That's all I know. Homework Equations The Attempt at a Solution I know these side lengths are related somehow.
  8. I

    MATLAB [Matlab]Copy Lower Triangle of symmetric matrix to Upper Triangle(or visa versa)

    Hello all! I just had a question about combining elements of matrices. In the MATLAB documentation, there was a function called triu and tril that extracts the upper and lower components of a matrix, respectively. I was wondering if there was a way to copy the elements of the upper triangle...
  9. S

    Find curve with tangent and normal lines that create a triangle with given area

    Homework Statement Find the implicit equation of the curve that goes through the point (3, 1) and whose tangent and normal lines always form with the x-axis a triangle whose area is equal to the slope of the tangent line. Assume y` > 0 and y > 0. Homework Equations Hint: ∫( √(a^2 -...
  10. S

    Circles in an equilateral triangle.

    Homework Statement Three triangles are placed into a circle; The vertices of the triangle are tangential to each circle. How do you find the ratio of the area of the circles to that of the triangle? Homework Equations pi r^2, 1/2(b)(h), sqrt3/4 * a^2 (2r^2). The Attempt at a...
  11. O

    Area between Triangle and Rectangle

    Homework Statement Consider a large triangle, the tip is located at the origo x=0, it is sloped at an angle θ and -θ relative to the x-axis, relative to the x-axis, its dimensions in x can be considered infinite. A large stripe/strip/band is placed on top of the triangle but perpendicular to...
  12. E

    Finding the resultant of two vector of an oblique triangle

    Homework Statement A car travels 20.0 km due north and then 35.0 km in a direction 60.0° west of north. Using a graph, find the magnitude and direction of a single vector that gives the net effect of the car's trip. This vector is called the car's resultant displacement. I am...
  13. R

    Two primes in a Primitive Pythagorean Triangle

    Let's recall the Euclidean Rule for Pythagorean Triangles: Let (m,n) be co-prime natural numbers (m<n), then h := n^{2} + m^{2} e := 2 m n d := n^{2} - m^{2} = (n - m) * (n + m) form the hypothenuse, the even and the odd leg of a primitive Pythagorean triangle (PPT) If we...
  14. F

    PF erased my problem anyways triangle problem

    Homework Statement [PLAIN]http://img832.imageshack.us/img832/5249/unledhbk.png The Attempt at a Solution Alright PF just erased all my work so here is my work without LaTex because I am too frustrated to do this all again Basically I found the vectors QP = <7,8,0> |QP|...
  15. Z

    Moment of inertia of a music triangle

    Moment of inertia of a "music triangle" Homework Statement Find the moment of inertia about an axis thru the centre of mass, perpendicular to the plane of an equilateral triangle consisting of identical rods of length 'l' and mass 'm' connected at their ends. Homework Equations...
  16. L

    Real Analysis problem (easy), Triangle inequality

    Homework Statement > a[1], a[2], a[3], .. , a[n] are arbitrary real numbers, prove that; abs(sum(a[i], i = 1 .. n)) <= sum(abs(a[i]), i = 1 .. n) Homework Equations The Attempt at a Solution I have uploaded my attempt as a pdf file, since I'm not too familiar with the...
  17. V

    Help Proving ABC is Acute Triangle with Altitudes

    I need help in this ques ! ABC is acute triangle. A1, B1, C1 are foot of altitudes. A1 is reflected about AC to get A2. Prove that B1, C1, A2 are collinear...i couldn't evn figure out how to solve it...but i need it just tell me the method no need to proove...or just tell me the idea how to...
  18. C

    Prove using the Triangle Inequality

    Homework Statement Show that: (|x+y|)/(1+|x+y|) ≤ ((|x|)/(1+|x|)) + ((|y|)/(1+|y|)) Homework Equations You are given the triangle inequality: |x+y| ≤ |x| + |y| The Attempt at a Solution (This is done from the result, as I haven't been able to find the starting point)...
  19. N

    Unit Vector Perpendicular to a Triangle?

    Homework Statement Given: P=(1,-2,3), Q=(-4,2,5) and S=(2,1-4) Find a unit vector that is perpendicular to triangle PQS Homework Equations Cross and Dot Product The Attempt at a Solution Correct me if I'm doing wrong. I have two solutions that I've thought: 1)What I...
  20. B

    Angles within a spherical triangle

    Hi Guys, need some assistance. I am sure what I am asking is trivial but i still need help. How could i find the angle within a spherical triangle (triangle formed on a sphere). Now this triangle has equal lengths on all 3 sides. Pleas help!
  21. M

    Proving Triangle ABC's CD + AE = AC

    Homework Statement Given a triangle ABC with ∠ B = 60°. The bisectors of angle A and C intersect BC and AB at D and E respectively. Prove that CD + AE = AC. Homework Equations The Attempt at a Solution I stuck on this question for hours already... what is the trick of proving...
  22. C

    Center mass of triangle in 3-D space

    Homework Statement So I have a triangle with points: A (4,2,0), B (3,3,0), and C (1,1,3). We are to find the point at which the three medians intersect in i,j,k format. I've found the midpoints of each side but I don't know where to go from there.
  23. P

    Gergonne Point of Triangle ABC

    Hi there. This is my first post here so please excuse any mistakes i may make. I was going thur my textbook, and looking at various problems, and before I began my homework a certain problem caught my eye. In the figure below the circle is tangent to the x-axis, to the y-axis, and to the line...
  24. C

    Point Charges on Equilateral Triangle - Need Geometry Help

    Homework Statement http://www.ridemtl.com Homework Equations F = k(q1q2/r^2)The Attempt at a Solution I know pretty much what to do for the problem, but I cannot get the right answer. I think my issue lies within what angles I am using for the components. Because it is an equilateral triangle...
  25. D

    Solving for the Sides of a Triangle with Given Perimeter and Side Relationships

    Homework Statement The perimeter of a triangle is 14 meters. One of the sides is one meter less than twice the shortest side. If the remaining side is 3 meters longer than the shortest side, what are the lengths of the sides of the triangle? Homework Equations The Attempt at a...
  26. G

    Solving a Triangle: b=17.8m & theta = 65°, Find a & c

    Homework Statement Solve the following right triangle. b=17.8m and theta = 65 degrees. (Right angle is at bottom left, C is hypotenuse, A is bottom leg, B is left leg, theta is opposite of B). Solve for a & c Homework Equations The Attempt at a Solution a= 8.3m c= 42.118m...
  27. R

    Epsilon-Delta Proof for Continuity of f + 2g at x = a

    Homework Statement Part of an \epsilon-\delta proof about whether or not f + 2g is continuous at x = a provided that f and g are continuous at x = a The Attempt at a Solution I've got the proof (I hope), but I'm uncertain about whether I can do the following...
  28. V

    In Triangle EFG find the value of f, if e=7.3cm g=8.7cm and angle E= 73 degrees

    Hi Everyone, I am looking for some help on this question In Triangle EFG find the value of f, if e=7.3cm g=8.7cm and angle E= 73 degrees This question is from the lesson "Cosine Law" and from what I understand you can use the cosine law if you have all three side lengths or 2 sides and...
  29. I

    Expansion with Pascal Triangle

    Hi guys, At a real loss here. I have a question that requires me to expend (1+x+x2)5 by constructing a pattern similar to that of the "Pascal Triangle". I understand the Pascal Triangle and know how to use with with expansions of two terms only (i.e. just (1+x)5) Again, I have really have...
  30. U

    Triangle 90<x<135 such that B is tangent

    Homework Statement In triangle ABC, the altitude from B is tangent to the circumcircle of ABC. Prove that the largest angle of the triangle is between 90◦ and 135◦. If the altitudes from both B and from C are tangent to the circumcircle, then what are the angles of the triangle...
  31. P

    Hi, How do I find the height of the triangle , the triangle is set

    Hi, How do I find the height of the triangle , the triangle is set at 30 degrees and the length is 5 meters any help would be appreciated.
  32. P

    Snells Law and a triangle prism

    A light ray in air strikes the flat side of a right angle prism at a right angle. The prism has 32 58 as the other angles with 32 degrees being in the bottom and the right angle being to the right of it. The light ray consist of two different wavelenghts. When it emerges at the face AB. It was...
  33. R

    Basic triangle plane geometry problem - impossible?

    Consider a point P inside a triangle ABC. Angle PBC is 10 degrees, angle PCB is 20 degrees, and angle BAC is 100 degrees. Find angle PAC. Question is that is this problem even solvable? I found it in an Olympiad training book...
  34. P

    Solving Inclined Plane Problems: Explaining the Triangle Relationship

    Hi, I have a terrible time when solving Inclined Plane problems when it comes to dividing the weight component into two. I can't see why, to find the perpendicular component I do the cos Theta of the weight and the parallel component I do the sin Theta of the weight. Can anyone, (maybe on...
  35. P

    Where Does the Less Than Symbol Disappear in the Triangle Inequality Proof?

    Im curios as to why the inquality is ||x+y||\leq||X||+||y|| but the end of the proof is =(||x||+||Y||)^2 where does the less than symbol disappear too
  36. R

    How do I calculate a triangle coordinate?

    1. Calculate the coordinate of a triangle's 3rd corner when 2 corner coordinates and area is given (in Surveying). Given: Area of triangle ABC = 14994sqm Corner B coordinate = +3541.620 (Y); -5467.650 (X) Corner C coordinate = +3300.580 (Y); -5503.150 (X) Calculate corner A's coordinates? I...
  37. F

    Find a constrained equilateral inner triangle of a triangle

    Hi, I would like to understand how I can calculate the inner circle center of any equilateral triangle that has for constraint that each of its bissectors must intersect one extremity of the (for now let's assume bigger only) main triangle. For helping understanding my problem and approach...
  38. R

    Stability Triangle of Forklift

    Hi I came across this: http://www.free-training.com/osha/forklift/Physics/54.htm Here I don't understand why the forklift will remain stable only when the CG is inside the triangle. If the CG is outside the triangle but still within the square formed by the four wheels of the forklift why...
  39. D

    Radius of a circle that intersects two points on a right triangle.

    Homework Statement I'm trying to figure out the radius of a circle that intersects two points on a right triangle. One side of the triangle is tangent to the circle and the other intersects it. I have attached an image that helps further explain what I'm talking about. Knowing what I have...
  40. D

    Radius of a circle that intersects two points on a right triangle.

    I'm trying to figure out the radius of a circle that intersects two points on a right triangle. One side of the triangle is tangent to the circle and the other intersects it. I have attached an image that helps further explain what I'm talking about. Knowing what I have listed in the image is...
  41. M

    What is Meant by By Symmetry in the Reverse Triangle Inequality Proof?

    Homework Statement I'm reading the proof for the reverse triangle inequality, but I don't understand what is meant by "by symmetry" Homework Equations The Attempt at a Solution (X,d) is a metric space prove: |d(x,y) - d(x,z)| <= d(z,y) The triangle inequality d(x,y) <=...
  42. A

    Can I Calculate a Power Triangle with Given Voltage and Current?

    This is an enquiry into whether something is possible, so the numbers might be rubbish to work with. If I apply a voltage of v=25sin(wt+0.2rads) to a circuit, with a resultant current of i=15sin(wt-0.5rads), can I work out all three sides of a power triangle? I've been working on it for...
  43. K

    Problems with finding moment of inertia of triangle

    Hi guys I am trying to find the moment of inertia of a thin triangle sheet as shown in the attached file, I couldn't so I looked at the solution and it said that x1 = ay/h and x2 = by/h. That is the only part I don't get, it seems to be some sort of ratio but I can't work out how or why its like...
  44. J

    Group theory - triangle rotation matrix problem? probably simple?

    I'm attempting to do some problems in a group theory exercise for the first time and am falling flat on my face. Here's the problem: "the molecule 'triangulum' consists of 3 identical atoms arranged in an equilateral triangle. Using a basis which consists of a single localised orbital on each...
  45. G

    What are the coordinates of the incentre of a triangle?

    what are the coordinates of incentre of a triangle if the three vertices are (a1,b1),(a2,b2),(a3,b3)?
  46. Femme_physics

    Finding the minimum length of a median in a triangle

    Homework Statement In a right triangle ABC, AD is a Median to BC (see drawing) Given: AB+BC = 4 A) Mark BD with an x, and express the lengths of the adjacent and opposite through x. B) Find the x for which the length AD is minimal http://img641.imageshack.us/img641/6798/abctriangle.jpg The...
  47. B

    How many rectangles fit in a triangle?

    Does anyone know how one could calculate the maximum number of whole rectangles that can fit into a triangle. Say you know the length of the sides of the triangle (t1,t2,t3) and the of the sides of the rectangle (r1,r2). Thanks.
  48. B

    Prove System of Forces Equivalent for Triangle Vectors

    Homework Statement Show that the system of forces represented by the lines joining any point to the angular points of a triangle is equivalent to the system represented by straight lines drawn from the same point to the middle points of the sides of the triangle Homework Equations...
  49. Y

    Pascal Triangle diagonal numbers

    Hi folks. Since people have already discussed tetrahedral and triangular numbers from the Pascal Triangle in nuclear physics, in peer-reviewed journals, this isn't a new idea. In the electronic system one can also find these numbers instantiated. In the left-step periodic table by Charles Janet...
  50. L

    Trig right triangle solving question How do you know if you should pick tan40 degrees

    Trig right triangle solving question How do you know if you should pick tan, cot, etc for the last part? if b = 2 , A =40 , find a,c, and B I found all of them except for c , how do you get c There's a part almost at the end that goes like tan40 degrees = a/2 and Cos 40 degrees = 2/c Why do you...
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