Triangle Definition and 1000 Threads

Homework Statement So I'm doing a physics problem, and I think I'd get the right answer if I solved this triangle. I don't know any angles. The base is 56 meters long, its height is 500 meters, and the difference between the other two sides is 4 meters. Can I figure out the sides based on this...

Homework Statement Homework Equations x^2 + y^2 = 9 A = 0.5xy x ≠ y The Attempt at a Solution x^2 + y^2 = 9 A = xy/2 (x + y)^2 = x^2 + 2xy + y^2 = 9 + 2xy = 9 + 4A A = ((x+y)^2 - 9)/4 Then I am lost. I need to find the area.

Consider a pole of 1 light second long in the ##y## direction (the vertical line(s) in the enclosed figure). It is moving in the ##-x## direction. According SR, the pole's length is not contracted because its length is not parallel to the propagation direction. However, given the time of flight...

Problem: Let $0<a<b$ i)Show that amongst the triangles with base $a$ and perimeter $a+b$, the maximum area is obtained when the other two sides have equal length $b/2$. ii)Using the result (i) or otherwise show that amongst the quadrilateral of given perimeter, the square has maximum area...

I know the Double Angle for Sine is: \sin(2x) = 2\sin(x) \cos(x) but from the triangle given, how do I figure it out? We did this in class, but the teacher just told a small amount of things, and then let us talk amongst each other to solve it. Nearly all the students were glossy eyed and did...

Triangle $PQR$ is an isosceles triangle with $PQ=PR$. Given that the angle bisector at $Q$ meets $PR$ at $A$ and that $QR=QA+PA$. Find angle $P$.

Problem: If A is the area and 2s the sum of three sides of a triangle, then: A)$A\leq \frac{s^2}{3\sqrt{3}}$ B)$A=\frac{s^2}{2}$ C)$A>\frac{s^2}{\sqrt{3}}$ D)None Attempt: From heron's formula: $$A=\sqrt{s(s-a)(s-b)(s-c)}$$ From AM-GM: $$\frac{s+(s-a)+(s-b)+(s-c)}{4}\geq...

in what point of the circumference: x2 + y2 = 1 the tangent to this, (to yhe circunference) form with the coordinate axes the triangle of smaller area?. answer ( +/-(sqrt2/2), +/-(sqrt2/2) ) Ok y2= 1-x2 Now I don't know in what point must i get the tangent?? I don't think it is in 0,0 I...

Gents, Thanks for all the guidance in the past with my work and brothers too. Can anyone help with these , see file attached

Hi, I am working on some MATLAB for my engineering classes and I need help with understanding a given diagram. In the attached diagram, I need help understanding how we determined the equations For example, I would like to know the equations for a triangle with the peak at 2/3L I know...

Homework Statement Consider the triangle of charges diagrammed below, for which d = 5 cm, q = 2 nC, and the +x-axis points to the right. What is the force Fvec on the 1 nC charge? Give your answer as a magnitude and a direction.Homework Equations F=K(q)(Q)/r^2 The Attempt at a Solution I...

Homework Statement Find the fluid force of a triangle with base of 6 ft and height of 4 ft submerged vertically into a body of water,vertex down, to a depth of 3 feet. Homework Equations from c to d W ∫ h(y) L(y) The Attempt at a Solution I set up the triangle on an x and...

Homework Statement Two charges of opposite sign and equal magnitude Q = 0.82 C are held 2.0 m apart as shown in the figure. Picture: http://gyazo.com/a78a049ce0a24ad464fd7bb99dffd665 A) Determine the magnitude of the electric field at the point P. B) Determine the electric potential...

Problem: Given that $a,b$ and $c$ are the sides of $\Delta ABC$ such that $$z=\log_{2^a+2^{-a}} \left(4(ab+bc+ca)-(a+b+c)^2\right)$$ then $z$ has a real value if and only if A)a=b=2c B)3a=2b=c C)a-b=3c D)None of these Attempt: I am not sure where to start with this kind of problem. I wrote the...

Suppose we have a quantity which can take discrete equally spaced values. Iteratively, we can increase or decrease this quantity by one quantum, splitting into two new worlds each time. After multiple iterations we have some indistinguishable worlds, as described by Pascal's triangle. As the...

Why do trigonometric ratios have to be related to the angle between the base and hypotenuse of a right angle triangle? I am trying to understand why I can't use these ratios to any angle of a right angle triangle. I try to do that in the attached document. It seems to work for all ratios...

Hello everyone, I have here one important abstract question which makes up some perplexity to my understanding. Attached to this post is one pic of F and two new introduced axes ( u and v ) . Let us for instance not consider them as perpendicular to each other. Now, if I...

Three charged particles are placed at the corners of an equilateral triangle of side L = 1.74 m. The charges are q1 = 3.63 µC, q2 = −8.05 µC, and q3 = −6.31 µC. Calculate the magnitude and direction (counterclockwise from the positive x axis) of the net force on q1 due to the other two...

I solved this many years ago, but after revisiting Trig in order to tutor my daughter, I revisited this to stimulate myself but am hitting a brick wall. Problem: A 4 inch square sits in a corner(picture x,y origin). A 12 inch ruler or line leans against the wall at an angle such that there are...

Show that the curve $x^3+3xy+y^3=1$ has only one set of three distinct points, $P$, $Q$, and $R$ which are the vertices of an equilateral triangle, and find its area.

I understand that S = P + jQ however I am confused how they got from that to the yellow box. Also, how did they get from the yellow box to the pink box and from the pink box to the blue box? Thanks

2 particles of charge q are placed at 2 vertices of an equilateral triangle of side a. An electric dipole is placed at the third vertex with its dipole moment orientated parallel to the opposite side of the triangle. a) Determine the magnitude of the torque on the dipole due to the electric...

A triangle hypotenuse given rectangle is rotated around one of their legs to generate a right circular cone? find the cone of greater volume. resp V= (2Sqrt(3)pi L^3)/27 It says hypotenuse given but it has no value According to the answer you can name it L

Inside a triangle $ABC$, there is a point P satisfies $\angle PAB=\angle PBC=\angle PCA=\lambda$. If the angles of the triangle are denoted by $\alpha$, $\beta$ and $\gamma$, prove that $\dfrac{1}{\sin^2 \lambda}=\dfrac{1}{\sin^2 \alpha}+\dfrac{1}{\sin^2 \beta}+\dfrac{1}{\sin^2 \gamma}$

Homework Statement Part (a): Find the intensity as function of ##\theta## and sketch it. Part (b): Find the intensity as function of ##\theta## and sketch it. Comment on first minima. Homework Equations The Attempt at a Solution Part(a) Convolution Method V_b = \frac{1}{2a}, 0 \leq...

Homework Statement Prove that the medians to the equal sides of an isosceles triangle divide each other into respectively equal parts Homework Equations The Attempt at a Solution suppose we have a triangle ABC where AB = AC. Let D be the point on AB in which the median intersects...

So hi, there's one little thing which I'm not understanding in the proof. After the inequality Spivak considers the two expressions to be equal. Why?!? I just don't see why we can't continue with the inequality and when we have factorized the identity to (|a|+|b|)^2 we can just replace...

Homework Statement If in any triangle r=r1-r2-r3, then which type of triangle is it? r1,r2,r3 denotes ex-radii. The Attempt at a Solution 4R = r1+r2+r3-r r2+r3 = 2R I can't figure out what to do next.

Homework Statement If in a ΔABC , \left( 1-\dfrac{r_1}{r_2} \right) \left( 1-\dfrac{r_1}{r_3} \right) = 2 then which triangle is it? r1, r2, r3 denotes ex-radii. The Attempt at a Solution I get this condition a^2+2b^2+2c^2+3bc=3ac+3ab Also \sum tan \frac{A}{2} tan \frac{B}{2} = tan^2...

Given a triangle $ABC$ such that $\angle BAC=103^{\circ}$ and $\angle ABC=51^{\circ}$. Let $M$ be a point inside triangle $ABC$ such that $\angle MAC=30^{\circ}$, $\angle MCA=13^{\circ}$. Find $\angle MBC$ with proof.

This is just a curiosity from my part: Has anyone know the proof of "Intersection of one internal angle bisector and two external angle bisectors of triangle is the center of an excircle."? I tried some things, but no luck.

Hi I have a problem understanding a figure in my lecture notes. The figure is the following one It shows the deformation of a triangular element from time t to time t+dt: So at t it is a isosceles triangle and at t+dt it is deformed. According to my lecture notes (page 16, eq. 28), the...

My daughter was given this problem in an exam. She could not do it and was never given the solution. I can do the problem using trig but she has not been taught trig yet. She says that it can be done without trig using a more simple method that she doesn't know. Could somebody please explain...

Homework Statement A rectangle is to be inscribed in a right triangle having sides 3 cm, 4 cm and 5 cm, as shown on the diagram. Find the dimensions of the rectangle with greatest possible area. Homework Equations 1. x^{2}+y^{2}=w^{2} in terms of w=\sqrt{x^{2}+y^{2}} 2...

The number of degrees in one acute angle of a right-angled triangle is equal to the number of grades in the other; express both the angles in degrees. So I have found the following answers : 810/17=47,05... degrees and 810/17=47,05... grades which gives 42,35... degrees Now, the real answer...

Homework Statement Lets say I have an equilateral triangle, and you are asked to calculate the net force on the top of the triangle Homework Equations Coulombs Law The Attempt at a Solution I know to use Coulombs law to find the forces acting on the top of the triangle, then since...

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

Triangle ABC with side lengths a,b,c please prove : $ \sqrt {ab}+\sqrt {bc}+\sqrt {ca}\leq a+b+c<2\sqrt {ab}+2\sqrt {bc}+2\sqrt {ca}$

1. A plane flies horizontally at an altitude of 5 km and passes directly over a tracking telescope on the ground. When the angle of elevation is \frac{\pi}{3}, this angle is decreasing at a rate of -\frac{\pi}{3} rad/min. How fast is the plane traveling at that time? Homework Equations...

Homework Statement The .274 and .88 was found using the equation of electrostatic force . Homework Equations K=q1q2/d^2 The Attempt at a Solution Would I just tan inverse of .274N and .88N which would be 17 degrees. However my question is: how to determine the reference pt: would...

Homework Statement There is the moment of inertia about an x and a y-axis named, I_{x}, I_{y}. Then there is the moment of inertia about the centroidal x and y-axis named, \overline{I}_{x}, \overline{I}_{y}. Often we can look up these values in a table (like the figure included) and apply...

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

Hello all! New to the forums, and I have a question for you. In my classes, we have been dealing a lot with proofs lately, so when I was working on an assignment, I figured I would try and find my own proof for something, just for the hell of it. I decided to tacle the area of a right angled...

Homework Statement Find the maximum area of a triangle with sides a\in (0,1] ,b\in [1,2], c\in [2,3]. Homework Equations The Attempt at a Solution I tried to make the area as a function of a single variable so that by differentiating I can get the answer. But it was...

A line divides an equilateral triangle into two parts with the same perimeter and having areas $A_1$ and $A_2$ respectively. Prove that $\dfrac{7}{9} \le \dfrac{A_1}{A_2} \le \dfrac{9}{7}$.

Homework Statement In triangle ABC with A as obtuse angle, AD and AE are median and altitude respectively. If BAD = DAE=EAC, then sin^3(A/3)cos(A/3) equals Homework Equations The Attempt at a Solution CE = a/2. Let DE = x. Then BD = a/2 - x. Let AE = p, AD = q. For ΔADB \cos...

Homework Statement Solving for base angles in a congruent triangle One of the base angles in a congruent triangle is 3x+5 The other base angle is unknown The remaining angle is x+16. Homework Equations See attached PDF The Attempt at a Solution Because two base angles in a...

I'm stuck on one aspect of the proof on page 105 of the 2nd edition. Equation 6.13 is necessary for the inequality to be an equality as it says but they never seem to account for inequality 6.11. Specifically, I don't see how this satisfies 2 Re<u,v> = 2 |<u,v>| Thanks for any guidance.

Homework Statement A molecule consists of three identical atoms located at the vertices of a 45 degree right triangle. Each pair of atoms interacts by an effective spring potential, with all spring constants equal to k. Consider only planar motion of this molecule. What are 6 normal modes and...

Hamming distance satisfies the triangle inequity that is for all x, y, u in c such that d(x,y) <= d(x,u) + d(u,y) where c is a code. Also when does the equality hold? My approach is Turning x to u by changing at most d(x,u) letters and turning u to y by changing at most d(u,y) letters. So...