For questions about triangles

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1answer
30 views

a question on “basic triangle at q”

Could someonehelp me to understand these sentences: A “basic triangle at $q$” will mean a triangle which has the sides adjacent to the vertex $q$ of equal length and an angle at $q$ of measure ...
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1answer
549 views

Finding a point of an isosceles triangle *OR* Find the coordinates of the start-point of an angled line

How do I find the coordinates ?/? (green star) given n, A (angle) and ...
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1answer
1k views

Calculate new graph point with coordinate and angle

On a Cartesian graph I have a point at x = 0 and y = 0. This point needs to move forward at a 30 degree angle. It should travel forward at this angle for 1.75 on the graph. What equation can I use to ...
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3answers
474 views

angle of an inscribed triangle

I have a scalene triangle inscribed in a circle, one of its sides $a$ is $2\sqrt3$ and the length $r$ from that side to the center is $1$. I need to find the angle $x$ opposite to the side given. ...
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2answers
170 views

Stuck on geometry proving

Points S and D are respectively the center of the circle circumscribed on the acute triangle ABC and the orthocenter of this triangle. Prove that ASBX, where X is the center of the circle ...
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2answers
436 views

Find the radius of the circle?

Three circles of equal radii have been drawn inside an equilateral triangle , of side a , such that each circle touches the other two circles as well as two sides of triangle. Then find the radius ...
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2answers
1k views

The sides of an isosceles triangle from the circumradius and inradius

I need to solve the following problem only by using Pythagoras Theorem and congruent triangles. Find the sides of an isosceles triangle ABC with circumradius R=25 and inradius r=12.
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4answers
5k views

two sides and angle between them triangle question.

is it possible to find the third side of a triangle if you know the lengths of the other two and the angle between the known sides? the triangle is not equilateral. we're using the kinect camera and ...
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1answer
3k views

How does this equation to find the radius from 3 points actually work?

I had searched online and found an equation that solves the radius of a circle from 3 points that are located on the circumference of that specific circle. Where I had found this formula did not state ...
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3answers
432 views

Counting right triangles with integral hypotenuse and given integral height

Let h = the height of the right triangle (an integer). Let c = the hypotenuse Let l = the other leg So l^2+h^2=c^2 I am trying to figure out, for instance, why ...
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3answers
1k views

how to prove DEF is an equilateral triangle?

ABC is an equilateral triangle,and AD = BE = CF,Prove DEF is an equilateral triangle.
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2answers
46 views

Inner product in $\mathbb{R}^2$ and angles of a triangle

Let $P_1,P_2,P_3$ be $3$ different points in $\mathbb{R}$, then $P_1,P_2,P_3$ form a triangle. What is the relation between the (one of the) angles of this triangle and $\langle P_2-P_1,P_3-P_1 ...
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0answers
123 views

Get value of angle with 45 degrees as maximum and 0 and 90 degrees as minimum

I want the calculate the "value" of an angle in such a way that: The angle of 45 degrees corresponds with the maximum value of 1 The angles of 0 and 90 degrees correspond with the minimum value of 0 ...
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1answer
79 views

Algorithm for a geometry-problem

In a system I'm building I'd like to have a "point" that hangs from two wires. The length of these wires is variable. So basically I would have a triangle, two sides of which are "varible". Could ...
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3answers
13k views

how to calculate area of 3D triangle?

I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. ...
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2answers
169 views

Find the ratio in which the circle divides each of the sides AB and AC?

A circle passes through the vertex A of an equilateral triangle ABC and is tangent to BC at its midpoint . Find the ratio in which the circle divides each of the sides AB and AC? Does the line ...
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2answers
2k views

circle inscribed into isosceles triangle

i am trying to solve following problem: suppose that legs AB=BC=30 in isosceles triangle,and center of inscribed circle divides altitude into 12:5 part,our aim is to find base,my problem is that i ...
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2answers
208 views

rational triangles and cosines

I've recently started to try working on exercises from this book on Diophantine equations before I need to return it to the library. This one has me slightly stumped. It asks to show that the cosine ...
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1answer
429 views

Finding the hypotenuse of Right Angle Triangle

The perimeter of a square is 48 inches. What would be the length, in inches, of its diagonal?
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3answers
609 views

Law of Sines will give a unique solution iff a > b?

Given a triangle ABC, with known sides a=BC and b=AC, and known angle A, we wish to find angle B. This is a typical application of the Sine Rule (Law of Sines). In some circumstances, the sine rule ...
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1answer
120 views

$C^2=A^2+B^2-2AB \cdot\cos(c)$ getting a different answer than creating a third triangle with the distance formula?

I have the following triangle: The side going up has a length of 96, the side going down has a length of 112. The angle closest to the center is 91 degrees broken up into 62 and 29 degrees from ...
3
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3answers
138 views

Radius of in-circle

The questions from geometry are most fascinating to me. As a parent I love to learn geometry and shapes from my son's textbook. I came across this statement about the in-circle: Let $m, n$ that are ...
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1answer
5k views

Getting the angles of a non-right triangle when all lengths are known

I have a triangle that I know the lengths of all the sides. But I need to know the angles. Needs to work with non-right triangles as well. I know it is possible, and I could have easily done this ...
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2answers
1k views

Given the vertex angle and side lengths of an isosceles, find the base

I need to be able to do this programmatically, so I'll need to be able to convert an example into algebra, but for the sake of hopefully having it make more sense to me, let's say the two sides are 15 ...
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3answers
284 views

Why Doesn't This Integral $\int \frac{\sqrt{x^2 - 9}}{x^2} \ dx$ Work?

I am trying to solve this integral, which is incorrect compared to Wolfram|Alpha. Why doesn't my method work? Find $\int \frac{\sqrt{x^2 - 9}}{x^2} \ dx$ Side work: ...
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1answer
98 views

A question on triangles

The radii $r_1,r_2,r_3$ of ex-scribed circles of the triangle $ABC$ are in harmonic progression. If the area of the triangle is $24$ sq.cm and its perimeter is $24$ cm, then what is the length of the ...
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2answers
125 views

Triangle Requirements based of triangle Inequality

In a Geometry course we are dealing with triangle inequality and two statements arose: "For any triangle, any side is smaller the the sum of the others." and "For any triangle, the largest side is ...
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1answer
2k views

probability of three random points inside a circle forming a right angle triangle

three points are randomly chosen on a circle. what the probability that 1.triangle formed is right angled triangle. 2.triangle formed is acute angled triangle. 3.triangle formed is obtuse angled ...
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2answers
223 views

Does “triangle” in English exclude degenerate triangles?

Just for fun read few problems on the projeteuler.net website. Number 276 found interesting: Consider the triangles with integer sides a, b and c with a ≤ b ≤ c. An integer sided triangle ...
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1answer
230 views

Heronian triangles

How to prove that all Heronian triangles can be found using formulas described here? I understand that the described substitution will give Heronian triangle, but how to prove that using the ...
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3answers
276 views

Elementary Geometry

The side of the square measures $1\ \mathrm{cm}$ , and $AC = 1\ \mathrm{cm}$, find the value of $AB$
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3answers
192 views

Vector path length of a hypotenuse

Consider the red path from A that zigzags to B, which takes $n$ even steps of length $w$. The path length of the route $P_n$ will be equal to: $ P_n = P_x + P_y = \frac{n}{2}\times w + ...
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3answers
403 views

Heronian triangle Generator

I'm trouble shooting my code I wrote to generate all Heronian Triangles (triangle with integer sides and integer area). I'm using the following algorithm $$a=n(m^{2}+k^{2})$$ $$b=m(n^{2}+k^{2})$$ ...
3
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1answer
299 views

Is there a way to tessellate an area using triangles and minimize/specify the number of unique triangles?

Is it possible to tessellate a planar surface from triangles but with the following constraints: density (average number of triangles) can be varied. a finite set of unique triangles are used for ...
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2answers
896 views

Integrate using Trigonometric Substitutions

Evaluate the integral using trigonometric substitutions. $$\int{ x\over \sqrt{3-2x-x^2}} \,dx$$ I am familiar with using the right triangle diagram and theta, but I do not know which terms would ...
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0answers
415 views

General formula for computing triangular gaussian quadrature.

While this is a simple question, I'm totally lost. Is there any general formula for generation of n-point gaussian quadrature over a triangle? I'll use this formula to generate a variable-point (7, ...
3
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2answers
418 views

Sierpinksi like triangle construction. How to find the number of triangles in each iteration?

So here is the question: If we look at the Sierpinski triangle (left column of attached image) and think about how many triangle's it takes to make the shape at each iteration we can get the sequence ...
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1answer
2k views

Ordering vertices in counter-clockwise manner in 3D space.

This is my first question in math and if I cannot get it right for the first time, please forgive me. I'm working on a simulation and I need to order vertices of a triangle in counter-clockwise ...
0
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1answer
145 views

Euclidean Geometry a triangle problem

In the three dimensional figure below, is there a way to prove that $$ \angle MNK = 90^ \circ $$ $\hspace{2.8in}$
11
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1answer
948 views

The Ellipse Problem - finding an ellipse inside a triangle

The problem statement is as follows: A triangle is dissected into six smaller triangles by its angle bisectors. Prove that the intersections of the angle bisectors of each of these smaller triangles ...
3
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1answer
260 views

How do you split a 90-45-45 triangle into equal area strips?

How do I find the values for $a_0, a_1, \ldots, a_n$ such that the triangle is divided into $n+2$ parts of equal area? In the above example, $n=2$. Let's assume that $a_i = 0$ means the line is at ...
0
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2answers
253 views

Given triangle ABC, if D is an interior pt and E is an exterior pt, segment DE intersects triangle ABC?

This is regarding neutral geometry I think. It seems to be obviously true but I struggle to prove it. My 'proof' goes by the following: since $E\notin\mathrm{ int}(\triangle{ABC})$, there exist an ...
15
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1answer
55k views

Solving Triangles (finding missing sides/angles given 3 sides/angles)

What is a general procedure for "solving" a triangle—that is, for finding the unknown side lengths and angle measures given three side lengths and/or angle measures?
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1answer
97 views

Sum of heights from a random point in triangle?

I've used an easy lemma for a problem about heights from a random point $O$ inside a equilateral triangle. It's easy to prove that $OA'+OB'+OC'=h$, where $A'$, $B'$ and $C'$ ...
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4answers
3k views

Solving a triangle given two side lengths and the measure of a non-included angle

Let's say given an angle A = 46 °, side a = 2.29 and b = 2.71 I figured that the angle B = 58.4 by saying: $$B = \sin^{-1} \left(\frac{ 2.71 \sin{46^{\circ}}}{2.29}\right)=58.4^{\circ}$$ But I ...
0
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2answers
946 views

Solving a triangle, given two sides and the measure of the included angle

Let say you have a triangle Angle A = 41 degrees , side b = 3.41 and c = 5.83 can you use pythagoras theorem to find the side a? and how can you find Angle B and C
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1answer
288 views

Find angles using the Law of Cosines

if you must find the Angle C based on the sides of a = 2, 3 b = 4,6 og c = 5, 9  I have used the formula: $$\cos (C) =\frac{a^2 + b^2-c^2}{2ab}$$ use, but I think i'm doing something wrong: ...
0
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1answer
863 views

Solving triangles and quadratic equations

When calculating the pieces in a triangle with only two sides and an intermediate angle is known, one must solve a quadratic equation. By solving the equation are 2, 1 or 0 solutions, as ...
2
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1answer
165 views

Similar Right Triangles and Incircles [duplicate]

Possible Duplicate: Triangle and Incircle In a setup of right triangles ABC, BDA, and BDC not unlike this diagram (click on the link, and ignore the written side measures and subtext in ...
0
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1answer
157 views

30 60 90 Triangle question.

A right triangle has a hypotenuse of $\sqrt{10}$, one of the legs is $x+2$, and the shortest leg is $x$. How do I find $x$? Thanks.