Triangle Definition and 1000 Threads

Homework Statement I know the area of a right angled triangle, I also know the ratio of the two non-hypotenuse sides. Is there anyway of finding the lengths? Thanks! Homework Equations I don't think there are any like Area = 1/2abSinC The Attempt at a Solution I obviously...

Hello,, I'm reading about beams in mechanics of matrials. But I'm a bit stuck because of one thing that I either don't understand or just don't comply with! So, here's a picture from the book: picture 003 It says that the center of mass should be at 2/3 of the length.. I tried to...

Homework Statement In a triangle ABC, with usual notation, if ##a^2b^2c^2 (\sin 2A + \sin 2B + \sin 2C) = λ(∆)^x## where ∆ is the area of the triangle and x ##\in## Q, find (λx). Homework Equations The Attempt at a Solution The usual notation is: a,b,c are three sides of the...

9 A Ladder 13ft long is leaning against the side of a building. If the foot of the ladder is pulled away from the building at a constant rate of 8in per second how fast is the area of triangle formed by the ladder, the building and the ground changing (in feet squared per second) at the instant...

Prove |x|+|y| ≤ |x+y| + |x-y| for all real numbers x and y. Some ideas I have is let a = x+y and b = x-y and apply triangle inequity Could anyone give me some direction? Thanks

The following inequality can easily be proved on ##ℝ## : ## ||x|-|y|| \leq |x-y| ## I was wondering if it extends to arbitrary normed linear spaces, since I can't seem to prove it using the axioms for linear spaces. (I can however, prove it using the definition of the norm on ##ℝ## by using...

Homework Statement Use vectors to demonstrate that on a circle any two diametrically opposed points along with an arbitrary third point(on the circle) form a right triangle Homework Equations Hint: assume without a loss of generality that the circle is centered at the origin and let v...

Homework Statement Three vectors A, B, C point from the origin O to the three corners of a triangle. Show that the area of the triangle is given by area = \frac{1}{2}|(B\timesC) + (C\timesA) + (A\timesC)| Homework Equations area of triangle with sides a, b, c = \frac{1}{2}|a\timesc|...

Suppose A1, A2 and A3 are closed convex sets, and let Δ be a triangle with edges F1, F2 and F3 such that A_1 \cup A_2 \cup A_3 = \Delta and F_i \cap A_i = \emptyset \text{ for } i=1,2,3 Prove there exists some point x\in \Delta such that x\in A_1 \cap A_2 \cap A_3 Figurative bonus...

Homework Statement Three rods each of uniform charge Q and length a are formed into an equilateral triangle. Given[Q,a,q] determine: 1. The voltage at the center of the triangle. 2. If a charge -q is placed at the center of the triangle determine potential energy. 3. Determine the initial...

Homework Statement Hey guys. Basically I have a wavefunction that looks like this http://imageshack.com/a/img843/3691/22r3.jpg I have to find: (a) The normalization constant N, of course by normalizing it (b) Find <x> and <x^2> and use this to find Δx. Homework Equations I'm just...

okay so I know that the area of the triangle is half the area of the parallelogram, ill try using pictures because this is a bit confusing to describe only with words: for example we have this http://farside.ph.utexas.edu/teaching/301/lectures/img243.png and then if we use the cross product of...

Here is the question: I have posted a link there to this topic so the OP can see my work.

Homework Statement If I have a triangle that has the hypo as √(u^2 +1) adj as 1 and oppo as u I did an integral with trig sub. So I used Homework Equations u = tan(θ) The Attempt at a Solution At the end of my integral I ended up with an expression (1/4)sin(2θ) When I...

The two shortest sides of a right-angled triangle, $a$ and $b$ satisfy the inequality \sqrt{a^2-6a\sqrt{2}+19}+\sqrt{b^2-4b\sqrt{3}+16}\le3. Find the perimeter of this triangle.

Homework Statement I got an answer as you can see in both pictures, but apparently it is wrong. What did I do? Homework Equations The Attempt at a Solution In this picture I found the y components of the electric field at C. Since the bottom 2 are the same i just doubled one of...

Given that triangle $ABC$ is congruent to triangle $CDE$, and that $\angle A=\angle B=80^{\circ}$. Suppose that $AC=1$ and DG=\frac{2\sin 10^{\circ}}{M+N\sin^2 10^{\circ}}. Evaluate $M+N$. .

hopefully this is the right place for this question, the first part is a trig/geometry question but it is really a integration question: i'm trying to find another way to compute d1 without using law of cosines because i don't know how to integrate (cos a)^.5, if someone knows how to do that...

Math Problem: Find the length of the third side of a triangle if the area of the triangle is 18 and two of its sides have lengths of 5 and 10. Which one of these are correct when I am working them out? If none of these are correct, then can somebody please help me solve this math problem...

Hello all, I am currently reading about the triangle inequality, from this article http://people.sju.edu/~pklingsb/cs.triang.pdf I am curious, how does the equality transform into an inequality? Does it take on this change because one takes the absolute value of 2uv? Because before the...

A triangle PQR has the following property: There is an interior point $A$ such that $\angle APQ=10^{\circ}$, $\angle AQP=20^{\circ}$, $\angle ARP=30^{\circ}$ and $\angle APR=40^{\circ}$. Prove that the triangle PQR is isosceles.

Homework Statement As ship is anchor off a long straight shoreline that runs north and south. From twi observation points. 15 miles apart on shore the bearings of the ship are N 31 ° E and S 53 ° E. What is the shortest distance from the ship to the shore. Homework Equations Sin θ Opp/...

I have the expression sin^{-1}(cosx) I'm not sure how to simplify this at all. I've never done a problem like this and it's in my textbook as a review question. A quick boot in the right direction would help

How do I find the volume of this shape? The bottom is a square in the xy plane where \(0\leq x,y\leq 1\). The object isn't a prism or pyramid so I am not sure what to do.

Homework Statement Three point charges have equal magnitudes, two being positive and one negative. These charges are fixed to the corners of an equilateral triangle. The magnitude of each of the charges is 2.9 µC. The lengths of the sides of the triangle are .02m Calculate the magnitude...

Homework Statement Uploaded Homework Equations Uploaded The Attempt at a Solution I actually need someone to check my work for 1.1 and 1.2. Is what I have done in 1.3 correct I mean it does not seem right?

Hi there, the problem says, an n-gon is circumscribed around a circle so the mid point of each side is tangent to the circle. Prove the triangle consisting of one side of the n-gon and the sides from the end points to the middle of the circle has area tan(pi/n) Cheers!

this is best I can figure for the triangle (shaded) but \vec{OC} looks like it has decimals in it.

P is an inner point of equilateral triangle ABC , given PC=3, PA=4,PB=5 ,please find the side length of the equilateral triangle

Consider the isosceles triangle circumscribed about the ellipse: Find the altitude of the triangle when its area is minimized.

Homework Statement I'm trying to express the function of a equilateral triangle as a function of the length of a side. All you know is the sides are all equal Homework Equations I have the answer but i don't understand (how and why they got there) and they used the A of a triangle as A=...

Homework Statement Let a be a unit vector and b be a non-zero vector not parallel to a. Find the angles of the triangle, whose two sides are represented by the vectors √3(a x b) and b-(a.b)a Homework Equations The Attempt at a Solution The third side will be equal to \sqrt{3}(a \times...

$\triangle ABC , \angle ABC=45^o,\,\, point \,\, D\,\, on \,\, \,\overline{BC} $ $and,\,\, 2\overline{BD}=\overline{CD},\,\, \angle DAB=15^o$ $find :\,\, \angle ACB=?$

Homework Statement I'm trying to solve the following problem : In △ABC, coordinates of B are (−3,3). Equation of the perpendicular bisector of side AB is 2x+y−7=0. Equation of the perpendicular bisector of side BC is 3x−y−3=0. Mid point of side AC is E(11/2,7/2). Find AC2. Homework...

Homework Statement Hi, I have inserted a picture of the problem: I have to find x, the altitude, or height of the triangle. x is the height of the larger triangle, and is perpendicular to the base of 13. It divides the base into segments of length 4 and 9. This was a question on...

Would this would the proper function, as described in the title of this thread, A = 1/2 x^2 \cos \frac{\theta}{2}? And suppose that the side x and the angle were changing with time, would the derivative, with respect to time, be \frac{dA}{dt} = x \cos \frac{\theta}{2} - 1/4 x^2 \sin...

Homework Statement The following is a geometry question I can't seem to get. "Consider an acute angle △ABC. Points D, E, F are mid points of sides BC, CA and AB respectively. G is the centroid of △ABC. Area of △AFG = 14, EC = 15/2. Perpendicular distance of F from BC = 6. Find BC2−AB2 "...

Please see the image attached. Does that have anything to do with directions? The right-hand rule?

Triangle ABC has AB=9 and BC:AC=40:41. What's the largest area that this triangle can have?

Homework Statement Taken from Spivak's Calculus, Prologue Chapter, P.28 b) Notice that all numbers in Pascal's Triangle are natural numbers, use part (a) to prove by induction that ##\binom{n}{k}## is always a natural number. (Your proof by induction will be be summed up by Pascal's...

Homework Statement An 800 g steel plate has the shape of the isosceles triangle shown in the figure. What are the x and y coordinates of the center of mass? https://www.physicsforums.com/attachment.php?attachmentid=13559&d=1208292919 Homework Equations x=1/M ∫ x dm [b]3. The...

I'm beginning to read Spivak's Calculus 3ed, and everything is smooth until I reach page 12. My question is marked, between line 2 and 3. Why there's such sign change suddenly? In fact I tried with simple line 4 case and it's not in fact equal. I'm assuming that a and b is valid for all...

the following diagram shows a circle with center O and a radius 4cm The points A, B, and C Lie on the circle. The point D is outside the circle, on (OC) Angle ADC=0.3 radians and angle AOC=0.8 radians (a) find AD I used law of sines \frac{4}{\sin{0.3}}=\frac{x}{\sin{0.8}} x \approx...

ABCDE is a pentagon,now please construct a triangle APQ ,and both of them must have the same area

Physical Problem -- triangle as a pool table Hello, can you please help me? It is an irregular triangle as a pool table: At point A, there is a small billiard ball. How should the bullet hit, that it hits first the band 1, then 2, and finally with the band 3, after a shock again arrives...

In a group of n people, each pair are friends or strangers. No set of three people are mutually friends. For any partition of the n people into two groups, there exists two people in a group that are friends. Prove that there exists a person who is friends with at most 2n/5 people in the group...

Hello MHB, I am working with an old exam that I don't get same answer. Line l_1(x,y,z)=(1,0,1)+t(2,-1,-2) and l_2(x,y,z)=(2,-5,0)+s(-1,2,1) intercept on point A also interpect on plane \pi:-x+2y-z+4=0 in point B and C, decide area of triangle ABC Progress: Point A: If we equal them we get...

Hi all, How would you determine the angle i in the following equilateral triangle. Thank you.

You have a thin rod of length $\ell$ and you cut it randomly into three pieces. Calculate the probability that the three pieces can form a triangle.

Homework Statement Use the triangle inequality to prove that \left| s_n - s \right| < 1 \implies \left| s_n \right| < \left| s \right| +1 Homework Equations The triangle inequality states that \left| a-b \right| \leq \left| a-c \right| + \left| c-b \right| The Attempt at a Solution...