# What is Equilateral triangle: Definition and 105 Discussions

In geometry, an equilateral triangle is a triangle in which all three sides have the same length. In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°. It is also a regular polygon, so it is also referred to as a regular triangle.

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1. ### Electric field at the center of the equilateral triangle

I've found the distance from each point to the center, which is equal to r=20x1.732/3 = 11.55 cm. I find out that E2 and E3 due to -4µEyC on x-direction canceled each other. The E2y = E3Y = EY = E2Ycos60 = E2/2 = [(KQ2)/r^2]/2 So the net E-field: E = E1 +E2y+E3Y =kQ1/r^2 + [(KQ2)/r^2]/2 +...
2. ### Justifying Equilateral Triangle AEF in ABCD

Given a rectangle ABCD and points E, F such that the triangles BEC and CF D are equilateral and each of them has only one side in common with the rectangle ABCD. Justify that triangle AEF is also equilateral.
3. ### Three Points at Vertices of Equilateral Triangle

I’m not sure of how to begin solving this problem. I attempted to draw a diagram and finding the components velocity of each initial velocity vector but this did not lead anywhere. Could so please have a hint?

5. ### MHB Prove ABC is an equilateral triangle

Prove $ABC$ is an equilateral triangle if $\dfrac{\cos A+\cos B+\cos C}{\sin A+\sin B+\sin C}=3\cot A \cot B \cot C$.
6. ### MHB Challenge question on equilateral triangle: Prove ∠DBA=42°

In an equilateral triangle $ABC$, let $D$ be a point inside the triangle such that $\angle BAD=54^\circ$ and $\angle BCD=48^\circ$. Prove that $\angle DBA=42^\circ$.
7. ### 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...
8. ### 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 $T$?
9. ### 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...
10. ### Triangle inscribed in a circle

Homework Statement [/B] In a circle with center S, DB is the diameter. The line AC goes 90 degrees from the center point M of the line SB. " What type of triangle is ACD? 2. Homework Equations The Attempt at a Solution I can see it is an equilateral triangle, but do not know how to explain...
11. ### Electric Field of Equilateral Triangle

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...
12. ### 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...
13. 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]
14. ### Calculating the area of equilateral triangle using calculus

Homework Statement Calculating the area of equilateral triangle using calculus. Homework EquationsThe Attempt at a Solution The area of the triangle is the area of the circle minus 3 times the area of the sector shown in (light blue). So, the target is to calculate the pink area first...
15. ### Three points at the vertices of equilateral triangle

Homework Statement Homework EquationsThe Attempt at a Solution The direction of motion of all the three particles are changing w.r.t. lab frame. But , their relative velocity remains constant. relative velocity = vb - va And the distance between the two particles decreases from a to 0. So...
16. ### Point charges in a equilateral triangle - typo in solution?

Homework Statement Three point charges each carrying a charge of 11.0 µC are located at the corners of an equilateral triangle of side 15.0 cm. Calculate the magnitude and direction of the force on each charge. Homework Equations k = 9.0x109NM2C-2 F = k⋅(Q1⋅Q2)/r2 The Attempt at a Solution...
17. ### I Integer Cevians - Equilateral Triangles

Is anybody familiar with any theory of integer cevians on equilateral triangles? More specificaly, I was trying to find something about the number of integer cevians that divide the side in integer parts. Like, the eq triangle of side 8 have cevian 7 dividing one side into 3+5. Only reference...
18. ### Find the third coordinate of a vertex of an equilateral triangle

Homework Statement Q. Prove that If (x1,y1) and (x2,y2) are the coordinates of the two vertices of an Equilateral Triangle then the coordinates of the 3rd vertex (X,Y) are $$X=\frac{x1+x2\pm\ √3(y1-y2)}{2},$$ $$Y=\frac{y1+y2\pm\ √3(x1-x2)}{2},$$ The Attempt at a Solution I used distance...
19. ### Moment of Inertia of equilateral triangle about vertex

Homework Statement A piece of thin uniform wire of mass m and length 3b is bent into an equilateral triangle. Find the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices. Homework Equations Slender rod, axis...
20. ### I Proof that lattice points can't form an equilateral triangle

From Courant's Differential and Integral Calculus p.13, In an ordinary system of rectangular co-ordinates, the points for which both co-ordinates are integers are called lattice points. Prove that a triangle whose vertices are lattice points cannot be equilateral. Proof: Let ##A=(0,0)...
21. ### Exploring the Benefits of Ionocrafts and their Equilateral Triangle Shapes

Hmmm maybe this goes here, maybe it doesn't. https://en.wikipedia.org/wiki/Ionocraft Here is a picture that depicts basically what I'm talking about. From what I understand, Ionocrafts work on N3L, and shoot ions down, pushing the craft up. This makes me think that the more charges you have...
22. ### Charged particle in centre of equilateral triangle

Homework Statement 3 charged particles located at equilateral triangles corners has charge ##q_1=q_2=q_2=4*10^{-6} C ## The 4th particle with charge ## q_4=3*10^{-4}## is placed at bisectors crossing. The distance between q1 and q4 is 3.46 cm .What is the net force on q4? Homework Equations...
23. ### MHB Prove Equilateral Triangle from Cosine Equality

Prove that if in a triangle $ABC$ we have the following equality that holds $2\cos A \cos B \cos C + \cos A \cos B + \cos B \cos C + \cos C \cos A = 1$ then the triangle will be an equilateral triangle.
24. ### Velocity of Three Charges Released from Equilateral Triangle

Homework Statement Three equal charges with charge q and mass m are placed into an equilateral triangle of side length L. Find the speed of each when they are infinitely far from one another. Homework Equations -ΔU =ΔK (since the electric force is conservative), U= 1/4πε Σq1q2 /r The...
25. ### Calculating Work to Move a Charge in an Equilateral Triangle

Homework Statement two particles with charges 4e and -4e are fixed at the vertices of an equilateral triangle with sides of length a. If k=1/4 pi Ԑ what quantity of work is required to move a particle with a charge q from the other vertex to the center of the line joining the fixed charges...
26. ### MHB Solve Proving 2 Triangles Cong. w/ Diam & Eq. Triangle (2-Col Proof)

Not sure how to solve considering nothing is given as perpendicular or bisected. Is anyone aware on how to solve this problem? ~S.R.K.
27. ### What is [s]motion[/s] moment of inertia of an equilateral triangle?

I am unable to find it.
28. ### {Geometry} Find length of the equilateral triangle

Homework Statement http://i.imgur.com/lnk7e0D.png CDE is an equilateral triangle inside a circle, with side length 16. FGH is also an equilateral triangle and F is the mid point of DE. Find the length of the side FGH. Should be expressed as Asqrt(B)-C. Where A B and C are positive integers...
29. ### Electrostatics: 3 Charges In An Equilateral Triangle

Hello, so this was a past assignment question that I attempted. I got the right answer but in an incorrect way (I guess my thinking was not based on the concept?) 1. Homework Statement Three point charges of charge Q = 10...
30. ### Resultant of 3 vectors along the sides of an equilateral triangle

Homework Statement Hi all, It is a homework problem, but I really don't quite understand the question. It reads- "3 forces of magnitudes 10N, 20N, and 30N acting on a point are parallel to the sides of an equilateral triangle, taken in order. Find their resultant"Homework EquationsThe Attempt...
31. ### Path of an object at the vertex of an equilateral triangle

Homework Statement There are three objects at the Vertices of an equilateral triangle that start movin towards each other at the same time with a speed v. Describe the path of the objects and the time taken for them to meet. Homework Equations V1=v3 - v2 Where all velocities are in...
32. ### Three electrons form an equilateral triangle

1. Homework Statement Three electrons form an equilateral triangle 1.00nm on each side. A proton is at the center of the triangle. What is the potential energy of this group of charges? Known Variables: s = 1.00 × 10-9m p+ Charge = 1.60 × 10-19C e- Charge = -1.60 × 10-19C r = s/√(3) = 5.77 ×...
33. ### Three charges at corners of equilateral triangle

Homework Statement Three point charges q,q and -q lie at three corners of an equilateral triangle of side length d with -q at the apex. If an electron is released from rest midway at the base (point P) what is its KE when its reasonably far away? Homework Equations V = kq/r, U = qV The...
34. ### Net Forces of 3 uneqaul charges of equilateral triangle

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > Three point charges are located at the corners of an equilateral triangle as Q1 in the top, charge Q2 in the left corner and charge Q3 in teh right corner. Each leg of the triangle has a length...
35. ### Electric Field of Point Charges in Equilateral Triangle

Homework Statement A point charge q =+6.4 \mu \mathrm{C} is placed at each corner of an equilateral triangle with sides 0.29 \mathrm{m} in length. What is the magnitude of the electric field at the midpoint of any of the three sides of the triangle? Hint: if you are careful to examine the...
36. ### Three Springs in an Equilateral Triangle

Homework Statement [/B] Three identical point masses of mass m each are placed at the vertices of an equilateral triangle and joined through springs of equal length and spring constant k . The system is placed on a smooth table. If the masses are displaced a little towards the centroid of the...
37. ### Total electric potential energy of equilateral triangle

Three charged objects, (+4 micro coulomb, -4 micro coulomb and +2 micro coulomb) are placed at the corners of an equilateral triangle with side length 2m. Calculate the total electric potential energy of the system... Guys Can you help me achieve a solution to this question? Thanks In Advance!
38. ### Center of mass of an equilateral triangle (Kleppner)

Homework Statement Find the center of mass of an equilateral triangle with side ##a## Homework Equations ## \vec R = \frac{1}{M} \int \vec r \ dm ## ## dm = \frac{M}{A} dx dy ## ## A = \frac{\sqrt{3}}{4}a^2 ## The Attempt at a Solution I set a pair of orthogonal axis ##(\vec x,\vec y)##...
39. ### Equilateral triangle ABC is inscribed in a circle

Homework Statement Can someone help me solve this, and teach me how to solve such problems in future? An equilateral triangle ABC is inscribed in a circle . Point D lies on a shorter arc of a circle BC. Point E is symmetrical the point B relating to the line CD . Prove that the points A, D , E...
40. ### Center E field of an equilateral triangle.

y/SUB]Homework Statement Determine the electric field at the center of the triangle. All sides are 15.6 cm. Vetex is 2.0 uC (Q1) while the bottom points are both -4.0 uC (Q2 and Q3). Homework Equations E = kQ/r^2 E = F/q The Attempt at a Solution Ecenter = E1 + (2)E2 = ? First calculate...
41. ### Kinematics Problem -- 3 particles at the vertices of an equilateral triangle

Here's the question: Three particles A, B and C are situated at the vertices of an equilateral triangle ABC of side d at time t = 0. Each of the particles moves with constant speed v. The particle at A always has its velocity along AB, B along BC and C along CA. At what time will the particles...
42. ### Electric Flux of equilateral triangle

Homework Statement What is the flux of the uniform electric field E=8 N/C through an equilateral triangle with the side a=1m, if the normal vector makes 60 degrees to the direction of the electric field. Homework Equations \phi=EAcosøThe Attempt at a Solution E=8 N/C A= √3/4 m^2 Is the ø in...
43. ### Mechanical force question on equilateral triangle

Homework Statement Three particles with masses m1=2.5kg, m2=1.2kg and unknown mass m3 are placed at the corners of an equilateral triangle of side 30.0cm. If the resultant force in x-direction acting on m1 is zero, find the net force acting on m1. Homework Equations F=(Gm1m2)/R^2...
44. ### Find the flux through the equilateral triangle with corners at

Homework Statement Find the flux through the equilateral triangle with corners at the points (1m,0,0), (0,1m,0), and (0,0,1m) in x,y,z space (measured in meters) for an electric field with magnitude E=6N/C pointing (a) in the z direction, (b) parallel to the line y = x. Homework...
45. ### Electric field strength at the center of an equilateral triangle

Homework Statement 3 rods each of length 1 meter form an equilateral triangle. Two rods have a uniform charge distribution of 8\times 10^{-6} C and the third of -8\times 10^{-6} C. What is the electric field strength at the center of an equilateral triangle Homework Equations \vec{E} =...
46. ### Electric Fields -- Charges at corners of equilateral triangle

Consider an equilateral triangle of side 15.6 cm. A charge of +2.0uc is placed at one vertex and charges of -4.0C uc each are placed at the other two, as shown in the diagram to the right. Determine the electric field at the centre of the triangle ANgle= 60 sides--> d1= d2=d3=0.156m...
47. ### Electric Force: Equilateral Triangle

Homework Statement Three charges, +Q, +Q, and -Q are placed at the vertices of an equilateral triangle of length "s" on a side. Find the magnitude and direction of the force on one of the +Q charges. Homework Equations ForceElectric=(K*q1*q2/d2) The Attempt at a Solution I've set...
48. ### Dot Product of Equilateral Triangle

Homework Statement In an equilateral triangle with sides u, v, w, where they are all unit vectors, find u dot w. Homework Equations u dot w = |u||w|cosθ The Attempt at a Solution The answer is ##\frac {-1} {2} ## cos(120) = -1/2 Elsewhere, I read the statement that since these are...
49. ### Coulomb's Law (3 charges in equilateral triangle)

Three charged particles are placed at the corners of an equilateral triangle of side L = 1.74 m. The charges are q1 = 3.63 µC, q2 = −8.05 µC, and q3 = −6.31 µC. Calculate the magnitude and direction (counterclockwise from the positive x axis) of the net force on q1 due to the other two...
50. ### MHB Find the area of an equilateral triangle

Show that the curve $x^3+3xy+y^3=1$ has only one set of three distinct points, $P$, $Q$, and $R$ which are the vertices of an equilateral triangle, and find its area.