Triangle Definition and 1000 Threads

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...

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)...

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...

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!

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...

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.

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...

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...

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...

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...

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...

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...

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...

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...

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.

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...

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...

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...

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

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...

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...

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...

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...

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...

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) <=...

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...

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...

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...

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

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...

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.

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...

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...

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...

Hello, As I believe is normal policy, please don't give me the answer to the problem :) I would, however, greatly appreciate a bump in the right direction. Homework Statement Triangle abc: side a=12, side b=15, angle C is increasing at 2 degress/minute. How fast is the length of side...

Two blocks are connected by a string-one on an incline, the rope draped over a pulley, and one hanging from the string. The smooth inclined surface makes an angle of 35 with the horizontal, and the block on the incline has a mass of 5.7 kg. The mass of the hanging block is 3.2kg. Find the...

Can someone help me understand why this is the case? I tried forming a cartesian equation for the two circles but there were too many variables that it would be too messy to compute. Otherwise I am rather stuck on how to do it. I would appreciate it if someone can explain how to prove this...

Homework Statement Given that: OA = 5s OB = 10 t P is on the middle of OA and AQ = 3 QB Find λ if BG = λ BP Homework Equations basic vector The Attempt at a Solution I have found AB, BQ, OQ, BP; all in terms of s and t. How to find λ? I've tried but always came back to...

Homework Statement Find the area of the largest rectangle that can be inscribed in a right triangle with legs adjacent to the right angle of lengths 5cm and 12cm. the two sides of the rectangle lie along the legs. Homework Equations N/a The Attempt at a Solution

Homework Statement an isosceles triangle with mass m and constant density is placed on an xy plane with base on the y axis. its height ranges from (0,-b/2) to (0,b/2) and its height is (a,0) Find its center of mass. I know that its density is equal 2m/ab. The Attempt at a Solution...

1. I am an architecture student and the assignment is to design a truss, set up the problem and solve it using graphic statics. I think I did it correctly using the graphical method but I am interested in solving it mathematically. Did I set the problem up correctly in my diagram and if so...

Homework Statement Prove the Triangle Inequality Theorum using the coordinate system. Homework Equations The corners of the triangles will be at (x1,y1), (x2, y2), (x3,y3) The Attempt at a Solution The proof that I know is proving that |x+y|<=|x|+|y|: -|x|<x<|x|, and...

So i have the points A=(1,0,1) and B=(1,-1,0) and the third corner lies on the line L:(x,y,z) = (t,t,t) and i need to find a triangle with the minimum area possible. My initial approach was to calculate the vector BA and BC and then apply both vectors in the area triangle formula...

Dear all, right now, I am doing my IGCSE and this question is in my coursebook. I can't think of any way to calculate it... It's part of the section circumference and area of circles. So must be some how solved using this. The semi-circle and the isosceles triangle have the same base AB and...

Homework Statement A right triangle ABCD is formed from four jointed links. The joint D at the midpoint of the hypotenuse is pushed until it lies on the leg AB. Homework Equations Find the height x when a = 50 mm The Attempt at a Solution give me a hint please cause I'm lost :mad:

I have the following question on metric spaces Let (X,d) be a metric space and x1,x2,...,xn ∈ X. Show that d(x1, xn) ≤ d(x1, x2) + · · · + d(xn−1, xn2 ), and d(x1, x3) ≥ |d(x1, x2) − d(x2, x3)|. So the first part is simply a statement of the triangle inequality. However, the metric...

[b]1. Homework Statement [ what is the distance from one corner of an equilateral triangle of sides a to the circumcentre? I can figure out the length from one corner to the opposite side to be sqrt3*a/2 but that's about it. I just can't see how to do this. thanks

Homework Statement How much work is needed to arrange three charges, Q, into an equilateral triangle? The particles are initially infinitely far apart. Take 'a' to be the length of each side of the triangle. Homework Equations U = {(kqq)/L} The Attempt at a Solution I was under...

Homework Statement I need help once again with this question below: Thanks, aeromat The Attempt at a Solution This is what I have so far: GP = GQ + QP GQ = GP + PQ GR = GP + PR GP + GQ + GR = GQ + QP[-] + PQ[+] + GP + PR + GP GP + GQ + GR = GQ + 2GP + PR I am stuck...

I am trying to get a different orientation on this triangle; specifically I want this output: ********** ********* ******** ******* ****** ***** **** *** ** * Here is the code that I have #include <iostream> using namespace std; int main () { int lines=10; int start =...