Triangle Definition and 1000 Threads

Homework Statement [/B] Three 3.0 g balls are tied to 80-cm-long threads and hung from a single fixed point. Each of the balls is given the same charge q. At equilibrium, the three balls form an equilateral triangle in a horizontal plane with 20 cm sides. Homework Equations F=kq1q2/r^2 F (of...

Just attempted another exam question. Would you mind correcting me if I am wrong? The question is A triangle ABC has sides of length AB= 3.5 m, BC = 5.1 m and AC = 4.2m. a) Calculate the size of the angle B and the size of the angle C, in degrees correct to 1 decimal place, in each case...

Hi, this would be my first post of many in recent times as I have my maths exam soon! I am doing a lot of past papers and I need some help understand some questions. In the triangle $$XYZ$$ angle $$Z$$ is a right angle. If $$XY$$= 15mm and $$YZ$$=8mm, calculate the angle $$Y$$, giving your...

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...

NOTE: I know the solution, but I challenge it. Specifically, I feel that the generally accepted solution to this problem is not intuitive. I have shown the accepted solution, and below that I have shown what I feel seems more intuitive (from a geometric standpoint)...

Prove for any triangle ABC that: cos(A)+cos(B)+cos(C)=1+4sin(\frac{1}{2}A)sin(\frac{1}{2}B)sin(\frac{1}{2}C) I tried using the half-angle formula on the right side to get: 1+4 \left(\frac{1-cos(A)}{2}\frac{1-cos(b)}{2}sin(\frac{1}{2}C)\right) {} which simplifies to...

Hi all, I am after some help to find out how to do the following: I have a triangular object (weighing around 40,000kg) which I can measure and weigh. I have 4 load indicators I can position anywhere beneath the object, these will give me a very accurate reading of the weight of the object at...

As shown in the figure below, triangle $PQR$ is divided into six smaller triangles by lines drawn from the vertices through a common interior point. The areas of four of these triangles area as indicated. Find the area of triangle $PQR$.

Hi! I'm stuck with the following problem: ----------------------------------- Calculate ∫∫ (x-y)*|ln(x+2y)| dxdy where D is the triangle with corners in the coordinates (0,0), (1,1) and (-3,3) ----------------------------------- I get the following lines that forms the triangle: y=-x, y=x...

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!

Homework Statement Hello. In class we learned how to calculate centroids of a triangle. For the y-coordinate we use the formula height/3 and for the x we use 2/3 * base Homework Equations In the diagram, If I want to calculate the y coordinate , I do 72 (which is the proposed height)/ 3 ; only...

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)##...

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...

$\int \, \int_{D}^{} \, y^3 dA$ D is the triangular region with vertices (0,1), (1,2), (4,1) i can't get past this problem. i drew the triangle but i don't know how to find the intervals... excuse my ugly drawing :p

Is anyone versed enough in Power transformer DGA and Duval triangles to know what the implications of the different regions might be? I've Googled and found many documents about the subject, but none really seem to mention what the implications might be for a transformer that tends towards T3 as...

Let $a,\,b,\,c$ be the sides and $A,\,B,\,C$ be the opposite angles angles of a triangle. Show that if $ab^2\cos A=bc^2\cos B=ca^2\cos C$ then the triangle is equilateral.

The legs of chateti of a right triangle are 9 and 12 cm. Find the distance between the intersection point of bisectors and the point of intersection of the medians

I'm having my semester test tomorrow, and I got this task from my teacher to do before the semester test. : By decomposition of forces apply these formulas for a right triangle: Task1: An iceberg floats with the stream and wind. The power comes straight from the north with speed 3m / s. Draw...

Homework Statement I need to find the area of the square in the following figure: Homework Equations Basic Trig relations. The Attempt at a Solution I aimed to find the length of BC, but first I had to find the unknowns of the right triangle CDE, which are EC=5m, <DCE=36.86ْ , <DEC=53.13ْ ...

ok so in this program, if three valid sides are given it displays the area of a triangle otherwise it will ask the user to re enter sides. #include <iostream> #include <cmath> using namespace std; int main(){ double a,b,c=0; double s,A=0; cin>>a>>b>>c; cout<<"Enter three sides: "<<a<<"...

So I have calculated Sin(70°) = Opp / 30.816, in this equation Opp = 28.95757 BUT when I do Sin(X) = 28.95757 / 30.816 I result in 1.08422336464 when converted to degrees gives me 62.12° NOT 70° If I put Opp (a) (28.95757) and Hypotenuse of (30.816) into the following calculator it says 70°...

Two sides of a triangle are 4 m and 5 m in length and the angle between them is increasing at a rate of 0.06 rad/s. Find the rate at which the area of the triangle is increasing when the angle between the sides of fixed length is $$\pi/3$$ When the angle is $$pi/3$$, the third side is equal to...

compute the area of a triangle. write an if/else statement to check if the three sides provide a valid triangle. to make a valid triangle, all sides have to be positive and the sum of any two sides must be greater than the third. add a while loop so that if the sides are invalid the user is...

I want to know how did it arrive at the third line of this proof. I didn't get it. Thanks!

I already found the side lengths that's being asked in the problem. But the part that I'm having difficulty is the Proving part. Can you help me do that? Thanks!

For a certain triangle ABC, sin A = 12/13, tan B = 15/8, and the altitude to side AB is 60 units. Find the lengths of the sides and of the altitudes of the triangle. Again, I couldn't come up with an image of the triangle in question. Maybe you can provide me the picture of the problem so that...

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...

Homework Statement Find the absolute maximum and minimum values of f(x,y) = y^2+x^2 -4x + 11 on the set D where D is the closed triangular region with vertices (8,0),(0,4) , and (0,-4) . Homework EquationsThe Attempt at a Solution [/B] fx = 2x - 4 fy = 2y Critical point = (2,0) The...

Please take a look at attached diagram displaying gradients of each line, please explain how m3 is obtained.

Homework Statement Find the area of the largest isosceles triangle that can be inscribed in a circle of radius 4. Solve by writing the area as a function of θ Homework Equations A=1/2 (bh) The Attempt at a Solution Given the side h and the hypotenuse 4, we can find the base of the smallest...

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...

Determine all triangles $PQR$ for which $\cos P \cos Q+\sin P \sin Q \sin R=1$.

Hi, i have a set of definition for a triangle shape: -3/4<x<3/4 -x/sqrt(3) + sqrt(3)/4 < y < x/sqrt(3) +sqrt(3)/4 The centroid of this triangle is at 0,0 i want to rotate this triangle by a certain degree from the centroid but i am not sure how, because if i just multiply it by cos or sin...

for the line y=4x-2 there is one perpendicular line of which will enclose a triangle on the lines and the values of the y-axis whose area is 8. What is the equation of this line? Well, I chose the x value to be the height of the triangle and that would make the base $$B=(4x-2)+2+\frac{1}{4}x$$...

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...

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...

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...

http://en.wikipedia.org/wiki/CHSH_inequality#Bell.27s_1971_derivation The last step of the CHSH inequality derivation is to apply the triangle inequality. I see there are relative polarization angles, but I don't see any sides have defined length to make up a triangle. Where is the triangle?

Homework Statement Find a nonzero vector orthogonal to the plane through the point P, Q,and R. (b) also find the area of triangle PQR P(1,0,1) , Q(-2,1,3) , R(4,2,5) Homework Equations -Cross product -Finding the Angle -Area formula The Attempt at a Solution My steps: 1. i found the...

Homework Statement Write a recursive function void recurTriangle ( int n, char ch ) which prints out an upside-down triangle. The parameter ch is the character to be used for drawing the triangle, and n is the number of characters on the first row. For example, if n is 7 and ch is ’+’...

Prove that if the sides of a triangle are prime numbers its area cannot be whole number.

Let $PQR$ be a triangle with $\angle P=90^{\circ}$ and $PQ=PR$. Let $A$ and $B$ be points on the segment $QR$ such that $QA:AB:BR=3:5:4$. Find $\angle APB$.

I am trying to solve the 'ant and honey problem on a spherical bowl' to find the shortest route between two points on a sphere when the path is constrained by not being allowed to pass higher than a certain latitude (so interrupting some great circles connecting the two points). I intuitively...

Hi, i am trying to model a triangle in a square cell based on its dimension. However, i have some problem with parts of the code, i think it might be the logic behind my programming or over definition with the code itself. i have attached the code. the problem lies with the second half of...

Homework Statement For the vectors in a Triangle, with a = 16, b = 12, and c = 20 what are (a) the magnitude and (b) the direction of A x B (c) the magnitude and (d) the direction of A x C (e) the magnitude and (f) the direction B x C this is Vector Multiplication. Homework Equations...

If $Q$ is a point on the altitude $AM$ of triangle $ABC$, and that $\angle QBA=20^{\circ}$, $\angle QBC=40^{\circ}$ and $\angle QCB=30^{\circ}$, find $\angle QCA$.

Hey! I just started study landsurveying and got a task i don't figure out how to get the right answer. My goal is to find the length of one of the sides in a triangle, but i can not use pytagoras formula. Here is the formula i am supposed to use (dont care about the text, its norwegian)...

Find the smallest possible area of an isosceles triangle that has a circle of radius $r$ inside it. I cannot seem to find the relationship between the circle and triangle. Any hints? I'm thinking similar triangles, but I want to know if they're any other approaches before I try that.

Homework Statement Side ##a=4 cm##, altitude to side a is 3 cm , angle ##\alpha =60 °##. How can I draw that? Step by step Homework Equations The Attempt at a Solution

Homework Statement How to find area of an n-dimensional triangle using vectors? Homework Equations The Attempt at a Solution