For questions about properties and applications of triangles

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3answers
71 views

Triangle inequality and its equality

How do I prove this? $$|x+y|=|x|+|y|\Leftrightarrow xy\geq0$$ I tried to use the triangle inequality, but I didn't get so far... Thanks!
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2answers
105 views

Why can I not use an equation using proportions to solve this triangle problem?

It is difficult to see the picture of the problem. The question is "What are the lengths of AC and AB?" What is given is a right triangle, ABC. Angle B is 30 degrees and BC is 7.0 distance. The ...
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1answer
188 views

Competition math geometry question

The perimeter of triangle ABC is $36$, and its area is $36$. Compute $\tan\frac{A}2 \tan\frac{B}2 \tan\frac{C}2$. I found that the answer is $1/9$, but I was not able to find a reason for this. Could ...
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1answer
65 views

How to prove that $DE=EF +DG$ from this following triangle problem?

Given a right triangle $ABC$, where $C$ is a right angle. We choose points $G$ at $AC$ and $F$ at $BC$, and $D$ and $E$ at $AB$. We draw right triangles $AGD$ and $EBF$, such that $\angle AGD= ...
2
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1answer
83 views

Solution for the value of an angle of a triangle ABC

Find value of angle m< DBC Where $$BD=DC=AC$$ $$2(m\langle BAC)=14(m\langle ABD)=7(m\langle BCD)$$ I tried hard but im out of ideas now, I know the answer is 20 but I want to know how, thanks ...
26
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4answers
2k views

Two circles inside a right angled triangle!

The other day I was playing with Ms Paint drawing circles here and there - I coincidentally drew a circle inside a right angled triangle which I already drew. Strangely A problem struck to my mind ...
2
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1answer
27 views

tetrahedron height

I've got the next figure: Now I would like to calculate the height, so from D to the plane ABC. First, I've tried with a coordinate system, but it's to difficult to take these distances into ...
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0answers
105 views

solve this complex triangle question ?

,D,E,F are midpoint of triangle ABC on sides BC , CA , AB. The feet of the altitudes from A,B,and C are P,Q and R. h is the orthocentre and O is the circumcentre . Then prove 2OD=AH. The nine ...
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3answers
152 views

Finding area of sector inside an triangle

I have been asked this question from a junior and could not solve the question in a simple way. I am asking help on this platform. For a triangle $ABC$, Points $D, E$ on $AB$, where ...
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1answer
46 views

Calculate regular or equilateral triangle altitude with radius only possible?

I need to calculate the altitude of a regular triangle (equilateral) but i only have the radius (polygon radius) available (http://www.mathopenref.com/polygonradius.html). I have been searching for ...
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2answers
219 views

To find base and height of an isosceles trangle if sides and area are give

The area of an isosceles triangle is $60cm^2$ and the length of equal side is $13cm$. Find height and base.
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1answer
140 views

Length of median extended to the circumcircle

A triangle has side length $13,14,15$, and its circumcircle is constructed. The median is then drawn with its base having a length of $14$, and is extended to the circle. Find its length.
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0answers
99 views

Hijacked Malaysian plane position geometry

Sorry to get geeky in the midst of a tragedy and likely horrible crime, but does anyone know how they got this diagram showing the possible last known positions of the possibly hijacked Malaysian ...
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1answer
51 views

Show that 3 circles related to a triangle intersects at common point

We have triangle $ABC$ and points $D,E,F$ which lies repectively at $BC,AC,AB$. There are circles passing through $AFE$, $FDB$, $CDE$ show that they intersect at common point
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1answer
447 views

Maximum perimeter of an isosceles triangle inscribed in the unit circle?

So I have seen this question asked before but with variations (circle of radius 4, and an equilateral triangle) and so I am hoping for an answer on how to do this. After looking around I saw that ...
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1answer
33 views

Solving integral including a triangle

How can I solve this integral? Image link: http://oi61.tinypic.com/2jeoga1.jpg I tried to solve it: x^2/2 from 4 to 0. [(4^2/2)-(0^2/2)]=8 but its wrong. Do I have to multiply base*height/2 because ...
-1
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5answers
221 views

Trigonometry Question (finding the sin, cos, cosec etc on a right-angled triangle)

For the right-angled triangle $\widehat{PQR}$, where $\overline{PQ} = 9\text{ cm}$, $\overline{QR} = 40\text{ cm}$ and $\overline{PR} = 41\text{ cm}$, give the value of: a) $\sin \hat{P}$ b) $\cos ...
3
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2answers
213 views

Find the maximum angle possible

$P$ is a point on the $Y-axis$ . Find the maximum possible value of $\angle APB$ where $A=(1,0)$ and $B=(3,0)$. Here is how I solved the problem. Suppose $P=(0,k)$ . Then using the cosine formula we ...
0
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1answer
41 views

Calculate an angle between time 00:00 and a mouse cursor position

I have to build a timepicker where user clicks on a clock like circle and it gives a time. Once I have cursor position I think that all I have to do is to calculate an angle between time 00:00 and a ...
1
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1answer
48 views

Similar Triangles with proportions

In $\triangle ABC$, $AB=8, BC=7, CA=6$, and side $BC$ is extended to point $P$, so that $\triangle PAB$ is similar to $\triangle PCA$. Find the length of $PC$.
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2answers
50 views

Prove that this is an isoceles triangle

I'm trying to solve a problem here. It says: "Prove that a triangle is isoceles if $\large b=2a\sin\left(\frac{\beta}{2}\right)$." $B-\beta$ I've tried to prove it but I can't Can anyone help me?
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1answer
44 views

Representation of a Triangle

In this document, a Triangle is represented as: $$ T(s,t) = B + sE_0 + tE_1\\for~all~(s,t)\in D=\{(s,t):s\in[0,1], t\in[0,1],s+t\le1\} $$ Can someone explain this representation of a Triangle?
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1answer
70 views

Regular pentagons inscribed in a triangle

I know that inscribing a square into a triangle has been researched a lot. But has there been any research on the problem inscribing a regular pentagon into a triangle? Can anyone tell me more on the ...
2
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2answers
49 views

Trying to triangulate from two (or three) known points.

If I'm at an unknown location, but I have visible points (monuments) that I know the location of, and I can measure the angle between them, I should be able to determine my location. I'm thinking ...
4
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1answer
285 views

Inequality in triangle involving side lenghs, medians and area

A, B and C are the vertices of a triangle. Denote $m_a$, $m_b$ and $m_c$ the medians from A, B and C. Prove the inequality: $$\sum_{cyc}{a^2bcm_a}\geq\sum_{cyc}{cS(a^2+b^2)}$$where a, b and c are the ...
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2answers
347 views

Scale sides of a triangle

If I have a triangle with sides A B and C, how can I scale the triangle down to one that has sides A + B = 1? E.g, if I have the triangle ABC where length of A = 45, length of B = 55 and length of C ...
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0answers
56 views

Triangle rotating freely around origo, need to calculate corners.

Lets say I have a triangle with corners $(-1, -2)$, $(0, 2)$ and $(1, -2)$. I specify a line that is exactly one side of the triangle, for example $(-1, -2)$, $(0, 2)$. Now, I rotate the triangle ...
0
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3answers
87 views

Finding the sides of Right Triangle when only angles are given

I have a question in which a Right angle triangle is given, one of the angle is 50 degree. Since it is a right angle therefor other two angles are 90degrees and 40degrees. The perpendicular of this ...
0
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1answer
42 views

How to extract all the points from a noisy surface?

I have points representing a bridge like in this picture: My goal is to get all the points that are in the red box. These points all share a common surface that is not necessarily planar. The ...
0
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1answer
2k views

Fourier Transform for triangular wave

Could someone tell me if I've worked this out right? I'm unsure of the process, especially the final parts where I convert it to a sinc function. Please let me know if I've made mistakes anywhere ...
8
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1answer
84 views

Trigonometric Substitution

I am having trouble with this problem even though everything I did seemed right to me since we went over a similar one in my class. I used the method of setting up a triangle, my hypotenuse is ...
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2answers
84 views

Proving the diagonals of a quadrilateral are equal

This is an easy question but it is troubling me a lot: $ABDC$ is a convex quadrilateral, with $AB=BC=AC$ and $\angle BDC=150^{\circ}$. Show that its diagonals are equal. I have tried fiddling with the ...
2
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2answers
457 views

Sine defined for a triangle inscribed in a circle with a diameter of one

Let a circle be drawn with a diameter of one (and thus a radius of one half). Then let a triangle with vertices A, B, and C be inscribed in the circle (i.e. points A, B, and C are arbitrary points on ...
4
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3answers
169 views

Prove Parallelogram Area Is Twice Triangle Area

I thought this would be easy but I can't seem to find the answer. Edit: I did my best to draw the diagram: $\overline{EC}=\frac{1}{3} \overline{AC}, \overline{AF}=\frac{1}{3} \overline{AB}, ...
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2answers
49 views

issues with geometry triangle

$4$ line drawn parallel to base of triangle such that they are equidistant.if the area of the most bottom part is 4 sq cm. find area of triangle? MY THOUGHTS : being weak in geometry i couldn't make ...
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6answers
498 views

New area of triangle if sides are halved

My question is that if we have a triangle, and we divide each of the side by 2 to get a new triangle, what will be the area of the new triangle in context to the original triangle? Please provide a ...
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1answer
232 views

How do I solve for the height of a triangle?

The basic triangle looks something like this: How do I solve for $h$? As an example, in one problem I was given $b = 45, c = 42, \angle C = 38^\circ$ I understand how $h$ divides $\triangle ABC$ ...
3
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2answers
81 views

Question about pythagorean triples

Given a,b,d natural numbers. Suppose (a, b) are two legs of a pythagorean triple. Also suppose (a, b+d) are two legs of another pythagorean triple. I'm looking for a way to show that given the ...
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2answers
407 views

Solving all possible triangles?

So we're doing oblique triangles -- Law of Sines and all that good stuff =). I have a bunch of problems that ask you to solve for "all possible triangles that satisfy the given conditions". For ...
3
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1answer
48 views

Odd and Even Triangles

I am about to make a report on the topic of characterization of line graphs then I came across the terms "odd triangles" and "even triangles". Does anyone know what these terms mean? To elaborate, I ...
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0answers
65 views

Howto prove that $\sum_{cyc}\cos\frac{A}{2}\cos\frac{B}{2}\le\frac{1+2\sqrt{2}}{2}+\frac{7-4\sqrt{2}}{R}r$

let $ABC$ is a triangle with inradius $r$ and circumradius $R$. Show that ...
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3answers
73 views

Can you find the the various values of a non 45-45- 90 triangle if only given hypotenuse and right angle?

I'm working on some homework. With a simple yes or no if you have a right triangle ABC with B being the 90 degree angle and not a 45-45-90 triangle and you have the value of the hypotenuse and the ...
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1answer
55 views

Determine missing angle in polygon

I'm trying to figure out this question: Determine the measure of angle a I'm guessing $a=96\unicode{0186}$ using the following work: $$a = 180 - 84 = 96 $$ ...
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0answers
44 views

Ratios of right triangle integer multiples to PI

It is known that in a right triangle with angles 30 and 60 degrees the cathetus at the 60 angle is equal to the 0.5 of hypotenuse. In other words an angle with cosine 0.5 is equal to PI/3. Is there ...
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3answers
177 views

Finding the Rate of distance between hands of clock

First, I think I don't understand the problem which asks about the greatest rate of change in distance between the tips of the hands of clocks. Does it mean where the increasing of distance is the ...
0
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1answer
182 views

Do degenerate triangles count? (2014 AMC 12B #12)

The problem is this: A set S consists of triangles whose sides have integer lengths less than 5, and no two elements of S are congruent or similar. What is the largest number of elements that S can ...
2
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1answer
117 views

Is it possible to reconstruct a triangle from the midpoints of its sides?

Take $ABC$ an arbitrary triangle, it is easy to take the midpoints $P$, $Q$, $R$ of sides $AB$, $BC$, $CA$, and we all know that the medians $CP$, $AQ$, $BR$ intersect at a point called the centroid ...
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3answers
183 views

An inequality for sides of a triangle

Let $ a, b, c $ be sides of a triangle and $ ab+bc+ca=1 $. Show $$(a+1)(b+1)(c+1)<4 $$ I tried Ravi substitution and got a close bound, but don't know how to make it all the way to $4 $. I am ...
2
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0answers
268 views

Triangle Packing-Problem

Theory and Question We define a normalized triangle $T$ as an ordered list of six points s.t. $p \in [0,1)$ for all $p \in T$. Let $T = [x_0, y_0, x_1, y_1, x_2, y_2]$ be a normalized triangle. We ...
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1answer
47 views

Given 3 points and there distances from eachother find a fourth point equidistant to the 3.

This question can also be asked: given a triangle, and its dimensions, whose vertices lie on the edge of a circle find the radius of the circle. I am not actually sure if there is enough information ...