Triangle Definition and 1000 Threads

Homework Statement The distances from the vertices of an equilateral triangle to an interior point P are √a, √b, and √c respectively,where a, b, and c are positive integers. Find the minimum and the maximum values of the sum a + b + c if the side of a triangle is 13. Homework Equations the...

Homework Statement I have a triangle with given vertices ABC. Given a vector that starts from A and intersects side BC, how can I find the point of intersection, p? Thanks Homework Equations The Attempt at a Solution

Homework Statement http://img23.imageshack.us/img23/9427/imageyakj.jpg AC+CB=24 The bisector = 8. Find angle DCB, i.e. x. Homework Equations The Law of sines, I think.The Attempt at a Solution

Homework Statement I think this must be really easy but I am not getting a visual for this triangle description. Let ABC be a triangle with \UparrowOA=a and /UparrowOB=b and /UparrowOC = c Where O is the origin . Homework Equations The Attempt at a Solution How can I...

My answer to this question seems close to that of the book but I have only solved for +1/2 and not the -1/2. Can anyone help? Many thanks. Homework Statement Q. The area of a triangle is \frac{-4m^2 + 4m - 1}{m}. Find the value of m via differentiation. Homework Equations The...

Homework Statement Triangle ABC has A (−1, 3,−3), B (2, 4, 6) and C (3, 0,−5). Use the scalar product to find the angle ACB. No pictures are given The Attempt at a Solution I have attempted the question by naming the triangle ABC with each angle opposite the line with the same...

Homework Statement Charges Q, Q, and q lie on the corners of an equilateral triangle with sides of length a. Charge q lies on the top corner with Q and Q on the left and right corners. (a) What is the force on the charge q? (b) What must q be for E to be zero half-way up the altitudeat...

Homework Statement Three point charges are located at the corners of an equilateral triangle as in the figure below. calculate the net electric force on the 7-nc charge. Each sides are .5 m. (q1=7μc) (q2=2 μc) (q3= -4 μc) ___1 __/__\ 2/____\3 Homework...

In the book by Keith Devlin on the Millenium Problems - in Chapter 6 on the Birch and Swinnerton-Dyer Conjecture we find the following text: "It is a fairly straightforward piece of algebraic reasoning to show that there is a right triangle with rational sides having an area d if and only if...

Homework Statement Consider a triangle ABC, where angle A = 60o. Let O be the inscribed circle of triangle ABC, as shown in the figure. Let D, E and F be the points at which circle O is tangent to the sides AB, BC and CA. And let G be the point of intersection of the line segment AE and the...

Homework Statement Find the area of triangle with vertices (-2,-2,2,2), (0,0,1,-1), (-1,-2,1,1) Homework Equations The Attempt at a Solution The only way I know how to find the area of a triangle is by finding half the parallelogram. I.e. A = (1/2)||u x v|| But this requires cross...

Each of ten segments has integer length and each one's length is greater than 1cm and less than 55cm. Prove that you can select three sides of a triangle among the segments.

I have attached a file with all needed information including the function and path of integration. My work seems right to me, but the correct answer is a^2. Will someone please take a look and show me where my misstep is.

Hey Guys, My question involves finding all of the forces acting upon each member. It is known that each side of the triangle has a length of l. It is also known that the force is acting at the very top of the triangle in the x direction (to the right) labelled as F. Attempt: I found moments...

Proving the "triangle inequality" property of the distance between sets Here's the problem and how far I've gotten on it: If you are unfamiliar with that notation, S(A, B) = (A \ B) U (B \ A), which is the symmetric difference. And D(A, B) = m^*(S(A, B)), which is the outer measure of...

Hi, I am trying to find the last vertex coordinates of a triangle given that Vertex 1 = (2,10) Vertex 2 = (3,6) Angle at Vertex 1 = 75.9638 degrees Angle at Vertex 2 = 70.3462 degrees. I have tried using the equations based on the length of each side, as well as using the cos dot...

find the area of the triangle with vertices (-1 2 -1 2) (-1 2 -1 1) and (2 -1 2 2) its 4 d Im confused thanks in advance

Given this seemingly simple problem of maximising the area of an isosceles triangle with perimeter equal to 1. What is the best approach and how will I find a result easiest (I know how to get the answer but I need to be able to do these problems fast, so please help me look for a quick method...

Homework Statement "At a given instant the legs of a right triangle are 8in. and 6in., respectively. The first leg decreases at 1in/min and the second increases at 2in/min. At what rate is the area increasing after 2 minutes?"Homework Equations A=\frac{1}{2}bh \frac{db}{dt}=-1...

In a triangle ABC, prove that $1<cosA+cosB+cosC \leq \frac{3}{2} $. One can easily prove that $cosA+cosB+cosC \leq 3/2 $, i.e. it can be proven to be true by 1. Using only the method of completing the square with no involvement of any inequality formula like Jensen's, AM-GM, etc. 2. By...

Let ABC be a triangle. Prove that $sin^2\frac{A}{2}+sin^2\frac{B}{2}+sin^2\frac{C}{2}+2sin\frac{A}{2}sin\frac{B}{2}sin\frac{C}{2}=1$. Conversely, prove that if x, y and z are positive real numbers such that $x^2y^2+z^2+2xyz=1$, then there is a triangle ABC such that $x=sin\frac{A}{2}...

Homework Statement The Attempt at a Solution I can't figure out how thales found the measurement of the length of this triangle without trigonometry since the sine and cosine ratios were not worked out until the 14th century I think. In any case, they certainly weren't known in...

Homework Statement Please see picture attached. Homework Equations The Attempt at a Solution If I use the pythagoras formula with the ratio I get the height as 3 yet it is longer than the side that is 4. Am I doing something wrong? Thanks.

I am trying to show $|(n+z)^2|\leq (n -|z|)^2$ where is complex $|(n+z)^2| = |n^2 + 2nz + z^2| \leq n^2 + 2n|z| + |z|^2$ But I can't figure out the connection for the final piece.

Homework Statement Write down the condition for the numbers p, q, r to form an arithmetic sequence. Homework Equations The Attempt at a Solution Have no idea, but I looked at the answer and they have assigned each letter with a given value (number). How is this possible?

Homework Statement In isosceles triangle RST, RS = RT. Which side of the triangle is the base? Which angle is the vertex angle? Homework Equations The Attempt at a Solution I believe the base is RT, and the vertex angle is S. I don't know the proper notation to name the line...

Homework Statement Show that if z_1,z_2 \in \mathbb{C} then |z_1+z_2| \leq |z_1| + |z_2| Homework Equations Above. The Attempt at a Solution I tried by explicit calculation, with obvious notation for a,b and c: my frist claim is not that the triangle inequality holds, just that...

Homework Statement The measure of the sides of an isosceles triangle are represented by x + 5, 3x +13, and 4x + 11. What are the measures of the sides? Two answers are possible. Homework Equations The Attempt at a Solution Well, I set up three different triangles, to account for the...

Three points are randomly chosen on a circle. Then they are connected together to make a triangle. What's the probability to see a 1. Right triangle 2. Triangle with all angles less than 90 degrees 3. Triangle with an angle bigger than 90 degrees I'm pretty sure to solve one of them...

Homework Statement Given an isosceles triangle - Length = L - Uniform Density = ρ - Width Varies from 0 at x = 0 to a at x = L I attached a picture of it. Homework Equations Have to show the width at position x is given by (a/L)x The Attempt at a Solution Now it is...

1. Homework Statement Sin(sec^-1(sqrt(x^2+16)/4)) 2. Homework Equations 3. The Attempt at a Solution I did the math and ended up getting x^2-1 as the opposite, but the answers on the back of the book say other wise.

Homework Statement Cos(Tan^-1(x)) Homework Equations The Attempt at a Solution Dont know how drawing a right triangle would do anything, don't know what to plug in.

I meet with a triangle integral where x+y≤1, and function is dependant only on x*y. I am wondering if there any possibility to relate ∫∫dxdyf(x*y)=∫d(x*y)f(x*y)g(x*y) or something similar? Or maybe there are some assumptions needed to relate like this?

Homework Statement http://img221.imageshack.us/img221/4861/figure1h.png Mod note: Fixed the image link. Consider the rigid object shown in this image. Four masses lie at the points shown on a rigid isosceles right triangle with hypotenuse length 4a. The mass at the right angle is 3m...

Hi Guys I've tried to do this problem but the answers are not being accepted is the math wrong? or did i forget a concept? Thanks for taking a look The triangle is set by Q1 on the top of the triangle Q2 on the bottom left and Q3 on the bottom right Calculate the magnitude of the net...

Geometry Triangle Congruence - **Edited to include diagram** Homework Statement Hi! The three simple geometry problems are in the attached photo. Sorry if they're difficult to read. I haven't seen this information in so long, and could use some help. :D Can you use the given information...

Homework Statement I have attached a picture of the problem. Homework Equations Singularity functions? The Attempt at a Solution So I am an electrical engineering student and got this mechanics course this semester and the teacher hasnt really explained anything, its almost like...

Prove that, if (c - b).a = 0 and (c - a).b = 0, then (b - a).c = 0. Show that this can be used to prove the following geometric results: a. The lines through the vertices of a triangle ABC perpendicular to the opposite sides meet in a point. b. If the tetrahedron OABC has two pairs of...

Prove that, if (c - b).a = 0 and (c - a).b = 0, then (b - a).c = 0. Show that this can be used to prove the following geometric results: a. The lines through the vertices of a triangle ABC perpendicular to the opposite sides meet in a point. b. If the tetrahedron OABC has two pairs of...

Homework Statement If the height of a triangle is five centimeters less than the length of its base and if the area of the triangle is 52 cm^2, find the base and the height.Homework Equations N/A The Attempt at a Solution height = h-5 base = h A=(bh)/2 52=(h(h-5)/2 52=(h^2-5h)/2 104=h^2-5h...

Homework Statement A point charge q = +2.0 µC is placed at each corner of an equilateral triangle with sides 0.23 m in length. What is the magnitude of the electric field at the midpoint of any of the three sides of the triangle? 3. I want to know if I did this correctly, or totally...

Vector A and vector B are expressed in component form. A = [2.32,-5.16,7.88] B = [-1.12,3.45,-12.8] The standard arrow representation of these vectors and that of can be arranged to form a triangle in a plane that represents the geometric equivalent of the subtraction operation. The...

Homework Statement Prove the triangle inequality for the following metric d d\big((x_1, x_2), (y_1, y_2)\big) = \begin{cases} |x_2| + |y_2| + |x_1 - y_1| & \text{if } x_1 \neq y_1 \\ |x_2 - y_2| & \text{if } x_1 = y_1 \end{cases}, where x_1, x_2, y_1, y_2 \in \mathbb{R}...

A FAQ is why the spacetime interval has a minus sign. A geometrical answer is that the interval is always the shortest path (the straight line) between two points. If we talk about spatial points, that interval is the hypotenuse of a right angle triangle, whose sides are the projections of...

Homework Statement Let a, x, and y be real numbers and let E > 0. Suppose that |x-a|< E and |y-a|< E. Use the Triangle Inequality to find an estimate for the magnitude |x-y|. Homework Equations The Triangle Inequality states that |a+b| <= |a| + |b| is valid for all real numbers a and...

If you have a triangle circumscribed around a circle, how do you find the area of that circle? Say that the triangle is an equilateral triangle with side length of 8 cm. I found the area of the triangle using Heron's formula: 16√3 cm^2. Apparently the answer is 16π/3 cm^2. I'm just confused...

Given an equilateral triangle ABC, P is any point inside it where PA = 3, PB = 4 and PC = 5. Find area of the triangle using the Law of Sines or Law of Cosines.

Homework Statement If A, B, and C are the vertices of a triangle, find the following. (A→B) + (B→C) + (C→A) The answer has to be given like this: _____ i + _____ j 2. Homework Equations (I think?) a+b=b+a a+(b+c)=(a+b)+c a+0=a a+(-a)=0 c(a+b)=ca+cb (c+d)a=ca+da (cd)a=c(da)...

Homework Statement The length of the sides of the acute angled triangle ABC are x-1, x and x+1. BD is perpendicular to AC. Then CD-DA equals? Homework Equations cosine law The Attempt at a Solution

Homework Statement An Isosceles triangle has two equal sides of length 10cm. Let x be the angle between the two equal sides. a. Express the area A of the triangle as a function of x in radians. b. Suppose that x is increasing at the rate of 10 degrees per minute. How fast is A changing...