Triangle Definition and 1000 Threads

Homework Statement 1. [/B]In the figure below, AB=BC=CD. If the area of triangle CDE is 42, what is the area of triangle ADG. See the attached figure Homework Equations I think we can start from area of triangle which is given by: Area of triangle CDE = ½ * CE * DE Or 42 = ½ * CE * DE...

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...

Homework Statement [/B]What are the lengths of sides NO and OP in triangle NOP? See the attached figure Homework Equations [/B]I don’t think that the inner triangle is the 30-60-90 triangle so we can't use the eq of 30-60-90 triangle. However we can use the pythagorous formula to...

This is quite an interesting puzzle. You know it's wrong but you don't know why by inspection: http://twistedsifter.com/2017/07/profs-use-this-puzzle-to-teach-lesson-about-problem-solving/ Can you figure out an easy way to inspect it? I spotted one way.

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...

I know that if a triangle have it edge // to each orther then it í the maximum triangle. Pls explain i don't understand hơ thí even possible

As a result of working on https://www.physicsforums.com/threads/area-of-hexagon-geometry-challenge.914759, this question occurred to me: Divide each side of a triangle into n equal lengths. Connect the ends of each length to the opposite vertex with straight lines, thereby forming 3n...

Homework Statement [/B] Given a general triangle ABC, find the geometric locus of points such that the three orthoprojection onto the sides of the triangle are aligned. Homework Equations Let's call A', B', and C' the orthoprojection of a given point M onto (AB) , (BC) , and (AC). M satisfies...

Homework Statement Homework Equations d(y)/d(x) --> max area area of triangle = 1/2 . base . height The Attempt at a Solution for number (2) [/B] x^2 + y^2 = r^2 --> circle equation base = 2R, height = y Area = 1/2 . 2R . y area = 1/2 . 4. √ (r^2 - x^2) area now is half of max = 2, so...

some formula related I tried to draw the problem can anyone give me clue how to solve it?

1. Find α(β) given that the sum of the 2 sides= ##(x+y)## and its third, ##z## is a constant for 0<β<180. You can imagine that there's two pieces of string connected between two points. One string is as long as the distance between the two points while the other string is longer. If you...

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 on the xy-plane to find all three sides. I then add all three sides. Correct? 2. Find the perimeter of the triangle that is formed by joining the...

I was investigating the number of unique grid points in a Cartesian coordinate system if I were to start at a corner (say coordinate 1,1,1), and make one step in each of the three positive directions (coordinates 1,2,1; 2,1,1; and 1,1,2). Now I went from 1 point to 3 points. I repeat the same...

Homework Statement The problem equation is contained in the picture. Homework Equations Pascal's Triangle is useful is this one. The Attempt at a Solution The difficulty I'm having is in going between lines 2 and 3 which I've marked with a little red dot. The closest I get to simplifying...

Determine the area of the painted hexagon, knowing that the area of triangle ABC is 120cm^2 IMG Link: https://m.imgur.com/a/WtdsW I tried using Heron´s formula, but just ended up with a bunch of terms and one more variable. Sidenote: I guess part of it is figuring out that the side lenghts...

Find the mass and center of mass given the following region R. R: triangle with vertices (0,0), (b/2, h), (b,0) Let p = rho p = k The letters b and h as given in the points make it hard to find the equation of the lines needed for the inner upper and lower limits. I have worked this out...

I have the following program that moves a wave on a string with fixed ends. The program solves the wave equation given a initial condition wave. The initial condition is a triangle wave splitting into two pulses. Here is the code written in Python: from numpy import * from matplotlib.pyplot...

Homework Statement How to rotate a triangle over a line? I have provided a attachment for it? Homework Equations Y= mx +c I don't know the eq for reflection The Attempt at a Solution My plan is find the eq of line. I have got points for the end points of the line but i don't know how to...

Can someone please help me with this question? Any help would be really much appreciated. Thanks all and have a great Easter!

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...

The vertices of Triangle ABC are A(1, 1), B(9, 3), and C(3, 5). Find the perimeter of Triangle ABC. I need to find the distance of AB, BC, and AC. I then must add all three distances to find the perimeter. Correct?

I have figured out the triangle's height and base, but I need to figure out sides a and b. I have tried Pythagorean theorem and similar triangle ratios, but it is not working out. Please help. See picture below. Thank you.

Prove, that for any triangle:\[ \sum_{cyc}\sin A - \prod_{cyc}\sin A \ge \sum_{cyc}\sin^3 A \]

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...

Homework Statement ##ABCD## is a square piece of paper with sides of length 1 m. A quarter-circle is drawn from ##B## to ##D## with center ##A##. The piece of paper is folded along ##EF##, with ##E## on ##AB## and ##F## on ##AD##, so that ##A## falls on the quarter-circle. Determine the maximum...

This is a problem I thought of, and I was wondering how to mathematically solve it with an equation. I tried calling one leg x. So the other leg, because of Pitagora's theorem, is: √(52 - x2) The area is equal to the product of the legs divided by two, so: 6 = (x * √(52 - x2))/2 12 = x * √(52...

Just wondering if anyone could confirm if I've headed in the right direction with these (a) Prove the triangular inequality: |x + y| ≤ |x| + |y|. (b) Use triangular inequality to prove |x − y| ≥ ||x| − |y||. (c) Show that if |x − a| < c/2 and |y − b| < c/2 then |(x + y) − (a + b)| < c. So for...

Homework Statement Suppose you have a Triangle with the vertices, (0,0) (1,1) and (0,1). Integrating along that path. I have some differential function dZ where Z = Z(x,y) Homework EquationsThe Attempt at a Solution [/B] If I need to integrate, then I need to find the limits of...

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)...

Point A(3, 4), point B(8, 5) and point C(7, 8) are located in quadrant 1 and form Triangle ABC. Note: Point A(a, b) Point B(c, d) Point C(e, f) Find the area of Triangle ABC using the formula below. A = (1/2)(a*d - c*b + c*e - e*d + e*b - a*e) I think this is just a plug and chug problem...

A right triangle is given. One leg is u units and the other leg is v units. The hypotenuse is given to be w units. If u = [2(m + n)]/n, v = 4m/(m - n), and w = [2(m^2 + n^2)/(m - n)n, show that (1/2)(uv) = u + v + w I must multiply u times v times (1/2), right? I then must add u + v + w. The...

A right triangle is given. One leg is u units and the other leg is v units. The hypotenuse is given to be w units. If u = [2(m + n)]/n and v = 4m/(m - n), show that w = [2(m^2 + n^2)/(m - n)n. Must I square u and v to show that w = [2(m^2 + n^2)/(m - n)n?

For b) area of AEF so one side is 7 - don't know how to get other 2 sides not sure if right triangle; don't think so how to use the data given since two of sides are slanted

Not sure how to use a single area and line segments that are same to calculate the areas and line segments for the areas.

In attached file, I understand 50 is the base; no idea how to use the 24 height to calculate length of ON - must have to do with property of right triangles?

Homework Statement In the drawing you can see a circumference inscribed in the triangle ABC (See the picture in the following link). Calculate the value of X https://goo.gl/photos/CAacV2dJbUrywfXv92. The attempt at a solution It seems I found a solution for this exercise with the help of a...

Homework Statement 1. Show that for an arbitrary uniform triangle ABC, with A at (x1, y1), B at (x2,y2), C at (x3, y3), the CM (xcm, ycm), is simply defined by xcm=(x1+x2+x3)/3, and ycm =(y1+y2+y3)/3 Homework Equations xcm = 1/M * ∫xdm ycm = 1/M * ∫ydm M = ∫dm = ∫δdA where δ = M/A = dm/dA...

I have to construct the triangle "J" only using protractor, ruler, compass and pencil. But I can't seem to find a way to figure out the angles. Please help.

Workings $\triangle ADE \cong \triangle CFE \left(AAS\right)$ $\angle AED = \angle CEF $( vertically opposite angles ) $\angle CFE= \angle EDA $( alternate angles ) $AE=EC $( E midpoint ) $ii.$ADCF is a parallelogram because diagonals bisect each other. Where is help needed How should...

The statement: In every ABC triangle, the laws of sine (a/sinA = b/sinB = c/sinC) & cosine (c2 = a2 + b2 -2*a*b*cosC) are valid, where a, b & c are the sides opposite to A, B & C respectively. Write a program that calculates and prints on the computer's screen, the length of c, and also the...

$\tiny{s6.12.7 Linkedin}$ a. Find the lengths of the ides of the triangle PQR. b. Is it a right triangle? Is it an isosceles triangle? $P(3,-2,-3), Q(7,0,1), R(1,2,1) PQ =\left|\sqrt{(3-7)^2 +(-2-0)^2+(-3-1)^2}\right|$ this is just an intro to vector calculus to get the basics of calc III

Rectangle $ABCD$ ,point $P$ on $\overline{AB}$ and point $Q$ on $\overline{DP}$ respectively given: $\overline{AB}=14,\overline{CP}=13$. and $\overline{DP}=15$, if $\overline{CQ}\perp \overline{DP}$ on $Q$ please find the area of $\triangle ABQ$

Can I have an opinion on this question, please? Personally I would use the cosine & sine rules to work out the angles then use trig to calculate the height. However, the question asks for Pythag to be used. Can someone please explain what method I should be using to answer this? Thanks Thanks Carla

Homework Statement It looks as if 50 degrees is an external angle of the triangle.So it should be greater than the two opposite interior angles (i.e x and the other one). But book tells a different answer. Somebody please guide me.Zulfi. Homework Equations No eq. Rule: Exterior angle of a...

< Mentor Note -- code tags have been added for better readability. In the future, please use code tags. Thank you. >[/color] 1. Homework Statement #include <stdio.h> void escreve_linha(int n) { int i; for( i = 0 ; i < n ; i++ ) { printf("*"); } printf("\n"); } void...

(0, 0), (3, 5), (1, 8) Find the slopes and equations for each line (0,0) ----> (3,5) = 5/3x (0,0)---->(1,8) = 8x (1,8)---->(3,5) = -3/2x+ 19 Then I set up the integrals (on x) Integral sign from 0 to 1 (8x-5/3x)dx + Integral sign from 1 to 3 [(-3/2x+19)-5/3x) dx I got 117/4 as an...

Any thoughts on the sketch? (Party) Many Thanks :)

Homework Statement line m2-to-m is 3km longer than line m1-to-m what are lengths for ##M~~M_2## and ##M~~M_1## Homework Equations pythagorean theorem hopefully can be used The Attempt at a Solution use the picture to your advantage in hopefully creating a valid system of equations. With...

Homework Statement A plane flying horizontally at an altitude of 3 mi and a speed of 480 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station. (Round your answer to the nearest whole...

I am having a very difficult time comprehending this exercise and any direction would be appreciated. Feel completely lost! Not necessarily asking for the answer just want to know how to tackle this. This program will output a right triangle based on user specified height triangleHeight and...