Triangle Definition and 1000 Threads

Homework Statement There is a triangle with sides $$ 3,3r,3r^2 $$ such that 'r' is a real number strictly greater than the Golden Ratio. Is this statement true or false...? Homework Equations $$Golden \space Ratio = \phi = 1.618... $$ The Attempt at a Solution Actually I have no clue at all...

In pascal triangle, if all the elements of a row(except 1 in both end) are divisible by the row number, then the row number is a prime. Or if the coefficient of binomial expansion (except 1's) are divisible by the power, then the power is a prime. It is inefficient to check all the coefficient...

hi can someone help me work this out. i think it has something to do with the exterior angle of a triangle is equal to the sum of the interior angles but i can't work it.

Dear friends, I am unable to find out the unknown angles for the following triangle which I attached with this post. Angle BAD and angle BCD are the unknown angles need to be calculated. Given that lines AB=BC=CD and angle CDE = 108 degrees From my calculations: angle ADC = 180 - 108 = 72...

Homework Statement Find the expression for the electric field at point M(a,a,0) if the linear charge density is known ( ##Q'## ) Homework Equations 3. The Attempt at a Solution [/B] I tried something like this and would like your feedback on it. I separated the triangle into three parts...

Homework Statement Given the points ##A (1, -1, 0)## and ##B (4, 0, 6)##, find the point ##P## of the line ##s## so that the triangle ##ABP## is a right triangle in ##B##. Calculate the area of the triangle. ##s : \begin{cases} x = 1 + 4t \\ y = 2 - 3t \\ z = 3 \end{cases}## ##\vec v_s = (4...

[FONT=Arial Black]Problem In the $\triangle ADC$ , $\angle DAC$ or angle $A$ is a right angle, E is the midpoint of AC . The perpendicular drawn to $AC$ from $E$ meets $DC$ at $B$ i.Drawn the given information in a figure & prove that $\triangle BAD$ is isosceles ii. $AC^2+AD^2=4AB^2$...

:D I have trouble in determining the ratio of the area of $\triangle PST$ in terms of $\triangle PQR$ In the triangle PQR $QT=TR$, $PS=1 cm$ , $SQ=2 cm$ , How should I be writing the area of $\triangle PST$ in terms of $\triangle PQR $ [FONT=Arial Black]What is known by me : Since...

Homework Statement Let AC=5 and BC=12. In the triangle ABC, with angle C=90, point M is in AC. A circumference with center M and radius r is tangent to AB and tangent to BC in C. Set r. Homework Equations This should envolve basic trigonometry, and Thales' theorem; but not sure ( if I knew the...

Show that if $a,\,b$ and $c$ are the lengths of the sides of a right triangle with hypotenuse $c$, then $$\frac{(c − a)(c − b)}{(c + a)(c + b)}\le 17 − 12\sqrt{2}$$

I am stuck with this problem: The right triangle shown with vertex P at the origin has base b, altitude a, and uniform density of surface charge σ. Determine the potential at the vertex P. First find the contribution of the vertical strip of width dx at x. Show that the potential at P can be...

Homework Statement The three vectors A, B, and C point from the origin O to the three corners of a triangle. Show that the area of the triangle is given by 1/2|(BxC)+(CxA)+(AxB)|. Homework EquationsThe Attempt at a Solution I know that the magnitude of the cross product of any two vectors...

Homework Statement Let P be a point on the sphere with center O, the origin, diameter AB, and radius r. Prove the triangle APB is a right triangle Homework Equations |AB|^2 = |AP|^2 + |PB|^2 |AB}^2 = 4r^2 The Attempt at a Solution Not sure if showing the above equations are true is the...

can some1 show me how to do this the answer to the first part is √x²+√16/x²

https://i.imgsafe.org/5172eee94d.jpg For a closer look click https://i.imgsafe.org/5172eee94d.jpg We know that the area of the sector should be $\frac{40}{360}$*$\frac{22}{7}$*$r$*r Any ideas on how to begin? Many Thanks:)

For a closer look click here Any Ideas on how to begin? Many Thanks :)

Homework Statement Find x[/B] Homework Equations a+b+c=180[/B]The Attempt at a Solution ADB= 65+65+50=180 How do I find x in DBC?

Homework Statement Find x[/B] Homework Equations a+b+c=180 [/B]The Attempt at a Solution So RP=RQ, the base angles are x and (146-x), normally the base angles are the same but in this scenario they are different. x+146-x+?=180

Homework Statement The three angles of a scalene triangle are x degrees, (x-12) degrees and (2x+6) degrees. What sizes are the angles?[/B] Homework Equations Triangle = a+b+c =180 Scalene = no equal size or angles[/B]The Attempt at a Solution So what do you do with (x-12) degrees and (2x+6)...

So I am working on this simple proof, but am confused about the term "external angle." The problem says that if ##a##, ##b##, and ##c## are external angles to a triangle, then ##a + b + c = 360##. However, is seems that the vertex of each triangle has two possible external angles, since there...

<<Mentor note: Missing template due to originally being posted elsewhere>> Hello everyone. I have the following problem: Determine the angles of a triangle where two sides of a triangle are formed by the vectors A = 3i -4j -k and B=4i -j + 3k I thought that I would find the third side being...

I am struggling with this question, it would be easy enough if the triangle was equilateral but that is not necessarily the case. Let (ha, hb, hc) be heights in the triangle ABC, and let Z be a point inside the triangle. Further to this, consider the points P, Q, R on the sides AB, BC and AC...

Currently revising for my A-Level maths (UK), there is unfortunately no key in the book; Given the triangle with sides a,b,c respectively and the area S, show that ab+bc+ca => 4*sqrt(3)*S I have tried using the Ravi transformation without luck, any takers?

I want to prove that the hypotenuse is the longest side of a right angled triangle. Could people check that the proof I'm giving is correct? Say the hypotenuse is of length ##c## and the other two sides are of length ##a## and ##b##. First of all, we obviously have: ##a^2 + b^2 > a^2 \quad##...

Homework Statement this is actually mohr's circle formula, forget about the theory,let's focus on the mathematics part. I couldn't understand why the tan( 2 θs1) = -(σx -σy) / 2τxy ? 2θs1 is outside the triangle Homework EquationsThe Attempt at a Solution theorically, tan(180-α )= -tan( α ) ...

Hello! I am currently in Calculus 2 and we are dealing with hydrostatic force. I get the integration that happens but I always seem to have trouble with solving the word problems. With this problem, I realize that I use integrate by making an infinite number of rectangles on the 2 triangles. I...

Let $a,\,b$ and $c$ be the sides of a triangle and $x,\,y$ and $z$ are real numbers such that $x+ y+ z = 0$. Prove that $a^2yz +b^2xz+c^2xy\le 0$.

Homework Statement In the figure Q image2.jpeg (attached), equilateral triangle ABC is inscribed in circle O, whose radius is 4. Altitude BD is extended until it intersects the circle at E. What is the length of DE? Solution figure is attached. They formed a right angled triangle & calling it...

In the above given triangle when θ = 0 then b=c But when θ = 90 then d=0 Since d is the projection of b How we can derive a generalised formula for d or c-d with respect to θ Plese may kindly be elaborated

Homework Statement An object is moving around the unit circle with parametric equations x(t)=cos(t), y(t)=sin(t), so it's location at time t is P(t)=(cos(t),sin(t)) . Assume 0 < t < π/2. At a given time t, the tangent line to the unit circle at the position P(t) will determine a right triangle...

B b-a D a c-b+a C b A Right triangle ABC, with the standard a, b, c side lengths. Angle BAC = 2u degrees. Point D is on the hypotenuse AB, such that: BD = b-a, angle BCD = 3u degrees. Calculate u.

In the derivation of triangle inequality |(x,y)| \leq ||x|| ||y|| one use some ##z=x-ty## where ##t## is real number. And then from ##(z,z) \geq 0## one gets quadratic inequality ||x||^2+||y||^2t^2-2tRe(x,y) \geq 0 And from here they said that discriminant of quadratic equation D=4(Re(x,y))^2-4...

Hmmm maybe this goes here, maybe it doesn't. https://en.wikipedia.org/wiki/Ionocraft Here is a picture that depicts basically what I'm talking about. From what I understand, Ionocrafts work on N3L, and shoot ions down, pushing the craft up. This makes me think that the more charges you have...

Homework Statement What is the sum of the angles of a spherical triangle formed on the surface of a sphere of radius R? The triangle is formed by the intersections of the arcs of great circles. Let A be the area of the surface of the sphere enclosed by the triangle. This question is a...

Homework Statement 3 charged particles located at equilateral triangles corners has charge ##q_1=q_2=q_2=4*10^{-6} C ## The 4th particle with charge ## q_4=3*10^{-4}## is placed at bisectors crossing. The distance between q1 and q4 is 3.46 cm .What is the net force on q4? Homework Equations...

the black triangle is given, and red triangle is me trying to work it out why is my trangle wrong? and what is the right triangle? someone is sliding down a slope, with 2ms-2 of acceleration (not actually given which direction, maybe I'm wrong there, but the person is acelerating at 2ms-2 down...

Prove that if in a triangle $ABC$ we have the following equality that holds $2\cos A \cos B \cos C + \cos A \cos B + \cos B \cos C + \cos C \cos A = 1$ then the triangle will be an equilateral triangle.

Homework Statement In this I tried to resolve the components. So first thing, I converted the 12kg into Newtons so it would be 117.72 Newtons. Then found the perpendicular distance which is to g: cos(30)x1 then multiply the answer by 117.2N to give the weight down as 102N. As the moment...

Hello everyone, I am trying to solve exercise 7.21 in the "Hobson, Efstathiou, Lasenby, General Relativity. An introduction for physicists." What is asked is to show that the parallel transportation of a vector, along a closed triangle on a 2-sphere, results in an vector orthogonal to the...

I think we can say that a straight line is a triangle in which sum of two side equals third side in which two angle equals 0° and the middle angle equals 180°, but can we say that a striaght line is a triangle with two angle equals 90°, I am saying this because my sister is not beliving that...

Can you suggest a book that discusses properties of triangles and circles? (Like properties and theorems on circumcircle, excircle, nine point circle, etc). Most of the geometry books are either to basic or too advanced. I have read a book on complex numbers by Liang Shin Hahn. But the...

Homework Statement kettletown is 27km from teatown and 32km from coffee town. The angle from kettletown to coffee town to teatown is 29o. Determine the two possible distances between teatown and coffee town. Homework EquationsThe Attempt at a Solution The only problem I'm having is trying to...

Given: A right triangle and all the sides of the triangle are whole numbers. Does this imply that all the sides of the triangle can only be found by using the Pythagorean triple formula? Another words, is it possible that a right triangle can exist with whole number sides that escape the...

Let $\alpha,\,\beta$ and $\gamma$ be the interior angles of an acute triangle. Prove that if $\alpha \lt \beta \lt \gamma$, then $\sin 2\alpha \gt \sin 2\beta \gt \sin 2\gamma$.

Homework Statement Evaluate ∫∫D sin(x) / x dA, where A is the triangle with vertices (0, 0),(0, 1),(1, 1). Homework EquationsThe Attempt at a Solution I've set up the integral, with x≤y≤x^2, 0≤x≤1 for the upper and lower bands of each integral. dxdy I'm not sure how to go about it though. I...

In a triangle $ABC$ with side lengths $a,\,b$ and $c$, it's given that $17a^2+b^2+9c^2=2ab+24ac$. Evaluate $\cos \angle B$.

Hi PF! A friend asked me to look at a problem, said it was on his mind. Rather than restate it here (since a picture helps) please check out the attachment. I drew a picture in tikZ and gave my attempt at a solution, but something in my gut feels the answer is infinite. I'd love to talk with...

Homework Statement Magnetic Field B is going into the plane. Bar is moving to the right with velocity v. Neglect resistance of the conducting bar and all contacts. a.) Determine the induced emf in the circuit. b.) To maintain the uniform motion of the conductive bar, there must be an external...

$\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}\\ find \,\, \angle C=?$

Homework Statement Three equal charges with charge q and mass m are placed into an equilateral triangle of side length L. Find the speed of each when they are infinitely far from one another. Homework Equations -ΔU =ΔK (since the electric force is conservative), U= 1/4πε Σq1q2 /r The...