Triangle Definition and 1000 Threads

Homework Statement Where is the center of mass of an isoceles triangle? Homework Equations xcm=∫xdV/V (where V is the volume of the triangle) The Attempt at a Solution The representation of the sides is what I'm confused with. Flipping the triangle to it's side is what's recommended to be...

I've attached the problem and my work. When I enter cos^1(6.890625) I get an error, but 6.9 is also not the answer and Does Not Exist is also not an acceptable answer. So where I am going wrong with this?

I was thinking of using Pythagoras here but it didn't get me far Any suggestions?

Homework Statement Determine the triangles where the sides are consecutive elements of a geometric sequence and the angles are consecutive elements of an arithmetic sequence. Homework Equations The Attempt at a Solution I don't really know how to approach this problem, what the solution would...

If triangle JPT ----> triangle J`P`T`, what is the image of P? The image of TJ ? Any help would be awesome. (Posted on behalf of Robbie Marsh.)

Consider the spherical triangle $\mathcal{P}$ with vertices $P_1 = (1,0,0)$, $P_2 = (0,1,0)$ and $P_3 = (1/\sqrt{3}, 1/\sqrt{3},1/\sqrt{3})$. Find the angles $\phi_1, \phi_2, \phi_3$ of $\mathcal{P}$ at $P_1, P_2, P_3$ respectively. I know the cosine angles are $\cos(\theta_1) = 0$...

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?

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?

Homework Statement Find the area of a triangle, assume that you don't know the formula of area of any other figure. Homework EquationsThe Attempt at a Solution Well, i was trying to figure out how to find the area of a triangle out of nowhere, but could not get it. I want to know how it was...

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...

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?

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...

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...

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?

Homework Statement Attached I understand the first bound but not the second. I am fine with the rest of the derivation that follows after these bounds, Homework Equations I have this as the triangle inequality with a '+' sign enabling me to bound from above: ##|x+y| \leq |x|+|y| ## (1)...

Homework Statement Solve the triangle with the given information: A= 40°, B= 20°, a= 100m Homework Equations The Law of Sines ##\frac{sin\left(A\right)}{a}##=##\frac{sin\left(B\right)}{b}##=##\frac{sin\left(C\right)}{c}## The Attempt at a Solution This is a AAS triangle. And since I'm given...

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...

Masses $m, 2m$ and $\sqrt{3}m$ are located at points $P_1, P_2$ and $P_3$ on a circle $C$ so that their center of mass coincides with the center of $C$. Find the angles of the triangle $P_1P_2P_3$.

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.

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...

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...

I have some questions about the curvature of space (NB not of spacetime) near a planet like Earth. Unambiguously defining space curvature requires choice of a coordinate system, so I choose the Swarzschild system. Here are my questions: Would constant-time hypersurfaces under the Swarzschild...

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] $$\gamma \approx - arg(V_{ub})$$ $$\beta_s \approx arg(V_{ts})+\pi$$...

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 $T$?

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...

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...

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...

Given a triangle with angles $\alpha, \beta, \gamma$ opposite respectively to the sides $a,b,c$. Show in at least two different ways, that the triangle is equilateral if and only if $ab \cos \gamma = ac \cos \beta = bc \cos \alpha$.

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...

Dear all, I was trying to prove that the area of a triangle is equal to the determinant consisting of the three points of the triangle. I got to the end, and something ain't working out. The signs are all wrong. In the attached pictures I include my proof. Can you please tell me how can the...

Greetings! Can someone please help me figure out how to calculate the second moment of area for a hollow isosceles triangle? Is there an equation available somewhere? Or can I simply subtract a smaller triangle from a larger one, using the equation I=bh3/36? (so I= b1h13/36 -b2h23/36) Also, is...

Homework Statement Completely solve this triangle. No calculators please. A=? B=Pi/3 C=? a=(1+sqrt(3)) b=? c=2 Homework Equations Cosine law: b^2=a^2c^2-2ac(cos(B)) Sine law: Sin(A)/a=Sin(B)/b The Attempt at a Solution b^2=-6 You can plug in 1/2 in (cos(B)) right away. Other attemps, don't ask...

This may belong to the computing subforum, let me know if this is more true than having it here in the math forum :) My questions are 1) Suppose there is a plane in 3D space and I have 3 points to define it: p1 = {x1, y1, z1} p2 = {x2, y2, z2} p3 = {x3, y3, z3} and I want to put a particular...

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...

Hello all, Below there is a problem: There are five points inside an equilateral triangle of side length 2. Show that at least two of the points are within 1 unit distance from each other. I have plotted such a triangle using "Geogebra", and attaching the picture. I know that if I create...

I think the following formula is so cool.

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...

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...

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?

PICTURE INCLUDED 1. Homework Statement A piece of wire is bent into an isosceles right triangle whose shorter sides have length a The wire carries current I. Calculate the magnetic field for point P. Point P is located on the Y-axis ( 0, √2a). Two corners of the triangle are are located at...

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?

$\textsf{Find the area of the triangle determined by the points }$ \begin{align*}\displaystyle &P(1,1,1), \, Q(-2,-7,-1), \, R(-7,-1,4)\\ \end{align*} \begin{align*}\displaystyle \vec{PQ}&=(-2-1)i&+(-7-1)J&+(-1-1)k&=-3i-8j-2k\\ \vec{PR}&=(-7-1)i&+(-1-1)j&+(4-1) k&=-8i-2j-3k...

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...

Homework Statement A circular coil with radius a is connected with an equilateral triangle on the inside as shown in the figure below. The resistance for each section of the wire is labeled. A uniform magnetic field B(t) is pointing into the paper, perpendicular to the plane of the coil. B(t)...

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...

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.

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

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😎

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...