Triangles Definition and 215 Threads

Homework Statement let be ABC a generic triangle, build on each side of the triangle an equilater triangle, proof that the triangle having as vertices the centers of the equilaters triangles is equilater Homework Equations sum of internal angles in a triangle is 180, rules about congruency in...

So it has come to my attention that 'different geometries' have different rules for the interior angles of a triangle... What are these different rules for Euclidean, elliptic and hyperbolic geometry? What I'm really wondering though is what knowing these rules about the interior angles tells us...

Homework Statement The point charges in the figure have the following values: q1=+2.1μC, q2=+6.3μC, q3=−0.89μC. Suppose that the magnitude of the net electrostatic force exerted on the point charge q2 in the figure is 0.57 N . Find the distance d and the direction (angle) of the net force...

Not sure how to solve considering nothing is given as perpendicular or bisected. Is anyone aware on how to solve this problem? ~S.R.K.

As seen in the drawing attached, there are two circles, the first circle will be a container to hold water and the outer is a second layer of aluminium, in between these will be insulator. What is the best way to work out minimum space lost by using triangles/sectors to fill this area? Having...

Homework Statement Prove that similar triangles have equal ratios (ratios of the sides) Homework Equations SSS, AAA, SAS, SSA The Attempt at a Solution I posted a rather messy and incorrect proof and problem statement prior to this and I wish to correct my mistakes now. The ratios of the...

Homework Statement Prove that the ratios of the sides of a right angle triangle ( for example hypotenuse divided by ankathete...) are equivalent to the ratios of the congruent triangles. I believe this problem amounts to showing that sin(alpha)=sin(alpha') and the same for cosinus and tangens...

[Prefix] When we do trigonometric substitutions (such as for the integral x^3/(a^2-x^2)^2), we say something like "let x = asinp for -pi/2 <= p <= pi/2" then we carry on and solve the integral. However, sometimes our answer is ugly and we get some term in our expression like "cosp"- so we draw...

Homework Statement In the coordinate plane let ##A_i=(i,1)## for ##l\leq i\leq15##, and let ##A_i=(i-15,4)## for ##16\leq i \leq 30##. Find the number of all isosceles triangles, where all three vertices belong to the set ##\{A_1,A_2, \cdots,A_{30}\}## Homework Equations Knowing the number of...

Seriously, I understand it sometimes, but when it hits me with something like this, I'm just baffled...

The question is part of a mechanical aptitude test. The correct answer is 2, but there is no explanation. I do not understand why is 2, and not "equal on both". Can anyone give me some clues?.

I have a small question regarding proposition 37 of the elements of Euclid. http://aleph0.clarku.edu/~djoyce/java/elements/bookI/propI37.html The only problem I got with the proof is the fact that we don't seem to prove that we do have parallelogram. We have a figure with 4 side and we know...

Hi guys, was wondering if anyone could help me solve this problem. Thanks!

Hey all, I need to know when two triangles intersect in a 3D environment, given the 3 points. Any help apreciate have been stuck on this for a long time,

From Apostol's Calculus Volume I, "Area as a Set Function" 1. Homework Statement : Right triangular regions are measurable because they are constructed from the intersection of two rectangles. Prove that all triangular regions are measurable and have an area of the product of one-half, their...

Hey Guys. I'm having a bit of a problem with my solving triangles book. I'm finding the book really easy but there's this one thing that I keep getting wrong. Whenever I'm working with degrees with decimal points my answer aways fluctuates slightly from the real answer. I must be doing something...

Given the image: http://i.stack.imgur.com/EJ3ax.jpgand that $x_0 = 1, y_0=0$ and $\text{angles} \space θ_i , i = 1, 2, 3, · · ·$ can be arbitrarily picked. How can I derive a recurrence relationship for $x_{n+1}$ and $x_n$? I actually know what the relationship is, however, don't know how to...

I've never really understood this bit of trig, I think I get it if there are two parallel angles (parallelogram). But, I do not understand how you go about when the triangles aren't in a parallelogram.

Homework Statement Dear Mentors and PF Helpers, Here's the question: Homework EquationsThe Attempt at a Solution Here's my solutions: Please let me know whether I'm right. Thank you [/B]

Homework Statement Problem 99 from "Kiselev's Geometry Book I - Planimetry": Two isosceles triangles with a common vertex and congruent lateral sides cannot fit one inside the other. Homework EquationsThe Attempt at a Solution The statement is obviously true. If we visualize each isosceles...

Homework Statement Homework Equations SinA/a = SinB/b = SinC/c The Attempt at a Solution a=38, c=44, ∠A = 35° What I have so far: sin(35)/38 = sinC/44 44sin(35) = 38sinC 44sin(35)/38 = sinC sinC = 0.6641 sin^-1(0.6641) ∠C = 41.6º Is this ∠C1? After this I don't know how to...

Hello mathematicians! I've recently completed a trigonometry course online and find the subject to be of great interest. I find the laws of sine and cosine fascinating and extremely useful and also, of course, Pythagoras theorem is beautiful as well. Firstly, I claim no superior knowledge...

Hello, I would need some help with drawing these 3 triangles for my homework. Would be nice if you could just help me to start drawing (what to do first) the right way. Thanks. Homework Statement a) Regular triangle: b - a = 3cm c = 6cm γ = 120° b) Regular triangle: a + b + c = 16cm α = 75°...

Hello, I would need some help with drawing these 3 triangles which are part of my homework. Would be nice if you could just help me to at least start drawing (what to do first) the right way. Thanks. 1) Regular triangle: b - a = 3cm c = 6cm γ = 120° 2) Regular triangle: a + b + c = 16cm...

The picture has the problem and my attempts, I need guidance. Thanks in advance

Hi Guys, This is my second post relating to my problem, But I've boiled it down to more simple trig. sadly, I still can't figure it out. See the sketch below; what I want to obtain is x as a function of R. the angle in red, θ is the same for the two corners. What is known: 1) two...

Hello, I'm going through Landau and Lifshitz "The Classical Theory of Fields" this summer with a friend and in section 4 I've come to a bit of a math problem. Assume you have an inertial frame K' moving at speed V relative to an inertial frame K in the x-direction. In order for invariant...

Find the maximum real value of $p$ if for any triple of positive real numbers $m,\,n,\,k$ that satisfies the inequality $pmnk>m^3+n^3+k^3$, there exists a triangle with side lengths $m,\,n,\,k$.

A solid has a circular base of radius 3. If every plane cross section perpendicular to the x-axis is an equilateral triangle, then it's volume is I keep on getting 18 root 3. But the answer is 36 root 3. Could I get some help? Thanks.

Homework Statement In triangle ABC, point L and M divides the sides AB and BC in the ratio 2:3 respectively. AM and LC intersect at point P. From point P a line parallel to BA is drawn intersecting at D. Find the ratio of AD:DC The Attempt at a Solution I have attached the picture of...

Homework Statement Find number of triangles which can be obtained by vertices of a regular polygon of n sides. The Attempt at a Solution I think it should be nC3 as forming a triangle requires you to select any 3 vertices from n available vertices. But I'm not sure whether this is correct...

Homework Statement Find all functions for which any tangent in first quadrant "forms" a triangle with constant surface P. (You can assume that y'<0) Homework Equations The Attempt at a Solution Now, I know I should somehow get to differential equation and then solve it but, I...

If you use this formula: ##s^2####\times####\sqrt{3}####\div4## it gives you the area of said equilateral triangle. I guess it's pretty neat i discovered it, but it doesn't seem very useful overall, anyone know any other uses for it?

Prove that in any triangle, if the angle bisectors of two angles are congruent, then the triangle is isosceles Before I give my proof, here is a lemma to it: If a pair of vertical angles both have angle bisectors, then all resulting angles are congruent. Given: Vertical Angles ∠2 and ∠4, and...

Hello. I came up with this problem while I was waking up this morning, and some of the finer aspects have me pretty confused. First off, I made the simplification of a square grid because I'm not yet ready to deal with non-square grids, but maybe we can get to that later. Here's where I got...

"When triangles are similar, ratio of corresponding sides is equal." "When triangles are similar, ratio of corresponding sides is equal." I was wondering if there is any theoretical proof for this statement or is it only experimental?

I need help solving for any other information about the red triangle. Due to the extremely limited information I already have, I can't use the Law of Sines (the angle is obtuse) or the Law of Cosines (gives no solution or non-real solutions for the information given) like I normally would. I...

Let the IQ of a triangle be the ratio \frac{\text{area of the triangle}}{(\text{perimeter of the triangle})^2}. This is a dimensionless number. Show that the smartest triangles are equilateral triangles.

Homework Statement A ball on a porch rolls 60 cm to the porch's edge, drops 40 cm, continues rolling on the grass, and eventually stops 80 cm from the porch's edge. What is the magnitude of the ball's net displacement, in centimeters? ball starts rolling here \/ rolls 60cm-> #----------#...

Homework Statement Prove in hyperbolic geometry: In the accompanying figure M and N are the respective (hyperbolic) midpoints of AB and AC and θ and ∅ are the indicated angle measures. Determine, with proof, which of the following is true: (1): θ=∅ (2): θ<∅ (3): θ>∅ ( stands for phi)...

With triangles, what is the least amount of data I need before I can start working out other data about the triangle such as angles and lengths of sides ect? I think it is at least 1 length and 2 angles or 2 lengths and 1 angle? What about triangles other than right angle triangles?

Hi everyone please help me with this homework question! i need to solve for the left hand side of the tiangle, i hope the image uploaded succesfully i hav been having trouble lately though :/ (Headbang)Yep if any clarrification is needed please reply and i will sort it out Thanks

I was wondering why similar triangles have the property that the ratios of the similar sides are equal. Or why the triangular functions (sin, cos,...) for a certain angle is fixed. They are related, and if I can find one of them, the other can be proved easily. I was thinking about the slope of...

Homework Statement I am given triangle ABC and a point X on the segment AB, one circle is inscribed inside triangle ACX and another inside BCX the two circles touch at point Y which lies on the line CX. show the inscribed circle of ABC touches AB at X Homework Equations I suppose you...

In a triangle $ABC$, the sides opposite to vertices $A,B,C$ are $a,b,c$ respectively. I have to prove $$ \frac{\tan\left( \frac{A}{2}\right)}{(a-b)(a-c)}+\frac{\tan\left( \frac{B}{2}\right)}{(b-c)(b-a)}+\frac{\tan\left( \frac{C}{2}\right)}{(c-a)(c-b)} = \frac{1}{\Delta}$$ $\Delta$ denotes the...

Homework Statement I have a couple of MATLAB questions hopefully you guys can help me out 40).The volume of a right prism is base area * vertical_dimension. Find the volumes of the prisms with triangles of problem 29 as their bases, for vertical dimensions of 10. I don't understand which...

I have hexagon ABCDEF (30 cm2) and point M inside. True: ABM = 3 cm2; BCM = 2 cm2; DEM = 7 cm2 ; FEM = 8cm2 How can I determine area of others two triangles? I know their total area, but how individually? Thanks very much and if you don't understand, write, I will try to write better...

Homework Statement 1. Given n non-parallel lines such that no three intersect in a point, determine how many triangles are formed? 2. Given n lines in total, of which m are parallel, how many triangles are formed? Homework Equations Combination nCr (n choose r) The Attempt at a...

I am reading "Mathematical Methods for Scientists and Engineers" by Donald McQuarrie. In his discussion of polar coordinates, he uses a geometric argument to derive the differential area element, which is of course rdrdθ. He shows an isosceles triangle whose two equal sides are r, and the angle...

I have a mesh with unstructured triangular grid. I need to find neighboring triangles of each vertex. How can I do it? Thanks before :D