For questions about properties and applications of triangles

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2
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2answers
16 views

2D geometric relation in a rectangle

I'm trying to implement the Sakoe & Chiba's global constraint for the Dynamic Time Warping algorithm but I'm stuck with a geometrical problem : I'm trying to find the value of d given a, b and c. ...
2
votes
1answer
24 views

Interior Angle Embedded in a Triangle Embedded in a Circle

With only knowing the angles of $B$, $C$, and $D$ (shown above), is it possible to find the interior angle $A$? And if so, how?
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0answers
54 views

Abc is a triangle

Abc is a triangle (drawing of the triangle with measurements up the side of each side) Make a full size drawing of triangle abc in the space below The line AB has been drawn for you. Leave in all ...
-1
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1answer
19 views

Area of a triangle with one given measurement [on hold]

The hypotenuse of an isosceles right triangle is 4 centimeters long. How long are its sides? Round your answers to two decimal places.
4
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2answers
42 views

Triangle with Ratio of Sides Equal to Ratio of Angles

In an equilateral triangle, the side lengths are in ratio 1:1:1, as are the angle measures. Are there also non-equilateral triangles in which the ratio of the side lengths is the same as the ratio of ...
2
votes
2answers
31 views

Maximum perimeter for triangle inscribed in circle

How to prove that isosceles triangle has maximum perimeter from all trangles inscribed in circle? I found that from all isosceles trinagles - equilateral has maximum perimeter: Maximum perimeter of ...
2
votes
2answers
46 views

how many possible acute triangles with perimeter given

How many possible acute triangles exist with perimeter 18? All sides are positive integers. The triangle (7,7,4) is the same as (4,7,7). I need the work in a way that a geometry 9th grade student ...
8
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6answers
476 views

Finding the largest triangle inscribed in the unit circle

Among all triangles inscribed in the unit circle, how can the one with the largest area be found?
3
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2answers
39 views

If $x-2y+4=0$ and $2x+y-5=0$ are the sides of isosceles triangle having area $10$ sq unit .Equation of third side is?

Okay, I know two sides of an isosceles triangle are equal . I have also taken out the intersection points of the lines given in the question . Other than this , I have no clue about how I will find ...
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0answers
16 views

Angle for sloped surface intersection

I'm not sure if this is the right SE site for this questions so apologies if it's not. But I've got a question about calculating angles that I can't seem to figure out the maths for. To add a bit of ...
2
votes
2answers
36 views

An equation involving ratios in a triangle.

In triangle $ABC$, if the incenter is $I$ and $AI$ meets $BC$ at $D$, show that $$\frac{AD}{ID}=\frac{AB+BC+CA}{BC}$$ I tried using similar triangles and got nowhere, couldn't find any use for the ...
1
vote
1answer
36 views

Minimum number of moves required to invert a triangular array of coins?

I cannot find an equation that works WITHOUT rounding. The idea is to find the minimum number of moves to invert a triangle that is made out of counters. The triangle is arranged so that the first row ...
28
votes
5answers
3k views

I think I see mysterious lines inside triangles—how to prove their existence?

Lately I've been fooling around with points inside a triangle and the sum of their distances from all sides. This was when I noticed a weird behaviour: For each point I chose there always seemed to ...
1
vote
1answer
29 views

Given the incentre of $\Delta ABC$ and the equations of the angle bisectors what is the locus of the centroid of the triangle $ABC$?

I got this problem on a test yesterday Consider $\Delta ABC$ with incenter $I(1,0)$. Equations of the straight lines $AI$, $BI$, and $CI$ are $x=1$, $y+1=x$ and $x+3y=1$ respectively and $\cot \left( ...
0
votes
2answers
65 views

Triangle whose side lengths and area are rational numbers [closed]

Does there exist a triangle with side lengths given by rational numbers $x$, $2x$, and $y$ such that the triangle's area is also rational number?
1
vote
1answer
30 views

If $\vec{AA_1} + \vec{BB_1} + \vec{CC_1} = 0$ prove that the triangle is equlateral.

The problem states that if $AA_1, BB_1$ and $CC_1$ are the altitudes of the triangle $\bigtriangleup ABC$ and $\vec{AA_1} + \vec{BB_1} + \vec{CC_1} = 0$ then the triangle is equilateral. My solution: ...
1
vote
2answers
67 views

Getting different answers using different methods in a geometrical problem

Problem statement: Given a triangle with side lengths 4 and 6, their corresponding opposite angles have a 1:2 ratio. Find the length of the third side. I solved the problem in 2 ways and got as an ...
0
votes
1answer
107 views

Help determining angle

Let $R$ be the triangle defined by $−x\tan(\theta) \le y \le x\tan(\theta)$ and $x \le 1$ where theta is an acute angle. Sketch the triangle and calculate \begin{equation*} \iint_R(x^2+y^2)\mathrm ...
1
vote
2answers
35 views

Help for a problem with inscribed triangles

If we have a triangle $ABC$ with $AB = 3\sqrt 7$, $AC = 3$, $\angle{ACB} = \pi/3$, $CL$ is the bisector of angle $ACB$, $CL$ lies on line $CD$ and $D$ is a point of the circumcircle of triangle $ABC$, ...
1
vote
4answers
31 views

Inequality for sides and height of right angle triangle

Someone recently posed the question to me for the above, is c+h or a+b greater, without originally the x and y lengths. I used this method: (mainly pythagorus) $a^2+b^2=c^2=(x+y)^2=x^2+y^2+2xy$ ...
3
votes
2answers
83 views

How to prove the the addition of tangent is the same as the multiplication? [duplicate]

If A,B,C are angles of a triangle show that: $$\tan A+ \tan B+\tan C = \tan A \tan B \tan C $$ I've tried this many times but I cannot seem to prove it, can someone show me how to solve this ...
2
votes
2answers
26 views

Triangle relationships

I was wondering if someone can help me actually. You see I came upon this book called Mathematics for Physics by Michael and Malcolm Woolfson. I a presently stuck on the very first exercise and I can ...
0
votes
2answers
32 views

Calculating the right angled triangle's cathetus

We just started learning the Pythagorean theorem at school and we got a pretty difficult assignment. 5 meter tall bamboo broke and the top of it touched the floor 2 meters from the base of the ...
0
votes
1answer
22 views

How to prove Thomsen's theorem?

Thomsen's theorem states that given a triangle ABC, choosing a point on AB (but not A or B) and doing the internal path parallel to AC till reaching BC, and then doing the path parallel to AB till ...
3
votes
3answers
49 views

Determine length from sketch

I have a simple problem that I need to solve. Given a height (in blue), and an angle (eg: 60-degrees), I need to determine the length of the line in red, based on where the green line ends. The ...
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votes
1answer
50 views

Please help with this question about angle of elevation and depression [closed]

A surveyor needs to determine the height of a building. She measures the angle of elevation of the top of the building from the two points, 38cm apart. The surveyor's eye level is 180cm above the ...
1
vote
1answer
46 views

What is the name of this (circumscribed) triangle?

I am meeting the following triangle more and more in my investigations of ideal triangles in the Beltrami Klein model of hyperbolic geometry. That made me wonder: is there a name for it? (And does it ...
3
votes
1answer
44 views

Triangle Center Midpoint

Consider the following construction of a triangle center: (The method could also be easily generalized to any shape with finite perimeter) For each point $X$ on the triangle, find point $X'$ such ...
2
votes
2answers
40 views

Is there a measure for how thin or squat a triangle is?

Is there a measure for how thin or squat a triangle is? Similar to eccentricity for ellipses.
2
votes
1answer
35 views

Is there an equidissection of a unit square involving irrational coordinates?

An equidissection of a square is a dissection into non-overlapping triangles of equal area. Monsky's theorem from 1970 states that if a square is equidissected into $n$ triangles, then $n$ is even. ...
2
votes
4answers
34 views

Triangle Inequality with Complex Numbers

I was wondering how to prove the triangle inequality with complex numbers: Verify that the function $d(z_1, z_2)$ is a distance funtion on $\mathbb{C}$ and also on any subdomain on $\mathbb{C}$. I ...
1
vote
1answer
91 views

The minimum perimeter and maximum height of a triangle under constraints

I'm developing a web application that consists of a calculator triangles. Although I am not a mathematician, with paper, derive and Geogebra I managed to get a lot of formulas to calculate a triangle ...
0
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1answer
37 views

Finding the lengths of this triangle?

please help, i'm to answer the question. The length of AB is 14.67106m. Please give working outs.
0
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0answers
24 views

Ideal Triangles and Klein Beltrami Disc

I'm trying to prove something with the ideal triangle in hyperbolic geometry and someone told me that the ideal triangle looks like a euclidean triangle inscribed in a circle in the Klein Beltrami ...
-1
votes
1answer
30 views

Geometry: Perimeter of triangle formed by intersections of tangents

I'm a bit stuck on the question below, and I wondered if anyone out here might be able to help: Construct a circle with a centre in O(0,0) and a radius of 5. Two tangents of the circle intersect in ...
0
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2answers
70 views

Hyperbolic Ideal Triangle

I have everything pretty much figured out everything but I need help proving the unique point formed by the three perpendiculars in the picture
0
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1answer
18 views

Finding the radius of excircles from a right angled triangle

Right angled triangles have 3 excircles, I'm struggling to find a formula which gives me the radius of all three excircles, I've been struggling with this for a while. I've done some googling and I ...
-1
votes
1answer
40 views

Generating a random num from a triangular distribution [duplicate]

http://en.wikipedia.org/wiki/Triangular_distribution#cite_note-1 under "Generating Triangular-distributed random variates" given that U is a number between 0 and 1, what happens if the a, b and c ...
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votes
0answers
9 views

Explain how to calculate the third vertex of a 2D equilateral triangle given two other vertices, using trigonometry

Before you comment that this has been asked multiple times, please read further. Given 3 arbitrary points: A(a, b), B(c, d), C(e, f), where AB = AC = BC, find C, knowing the values of A and B, using ...
1
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2answers
43 views

Find the acute angles of this right triangle.

I am having trouble finding the acute angles of this triangle. O is the intersection of the medians of the triangle and $OG = \frac{1}{2}OH$. Any suggestions?
1
vote
1answer
101 views

How to prove a triangle similarity problem

If I have a triangle $ABC$ with point $E$ lying on $BC$ and point $D$ lying on $AB$ where $AE$ is the height to $BC$ and $CD$ is the height to $AB$, how can I prove that triangle $ABC$ is similar to ...
6
votes
0answers
66 views

Number of ways to dissect a square into triangles of equal area

Monsky's theorem states that it is impossible to dissect a square into an odd number of triangles of equal area. If $n$ is an even integer, I am interested in the number of ways of dissecting a ...
2
votes
0answers
17 views

Statue and a flag distances

Next to a flagpole is a statue that measures 9m high. The upper end of the flagpole with the bottom of the statue form an angle of 53.13 degrees to the floor, and the upper end of the flagpole to the ...
1
vote
3answers
58 views

Why are trig functions defined for the unit circle?

Why did we ever need to define the trig functions of angles greater than 90 degrees or less than 0 degrees? What is the use of applying trig functions to such angles? If we apply the trig functions ...
0
votes
1answer
40 views

Finding the angle?

I have two circles which share a radius of R units, and each circle contains the center of the other circle. I found that the area of the segment would be, $\theta$ is the central angle between the ...
-1
votes
1answer
28 views

Incenter divide ratio

Given a triangle $ABC$ and angle bisectors $BD,CE$ which intersect at $O$ (incenter) . The ratio in which $O$ divides $BD$ is $3:2$ and it divides $CE$ in ratio $1:2$ . Find the ratio in which the ...
6
votes
2answers
73 views

The conjecture that no triangle has rational sides, medians and altitudes

I have found a conjecture that there is no triangle whose sides, medians, altitudes and area are all rational. I figure that someone must have already found such a triangle if one existed and yet I ...
1
vote
1answer
26 views

How many ways are there to break up the regular 9-gon into triangles by diagonals?

How many ways are there to break up the regular 9-gon into triangles by diagonals? UPD Guaranteed to be convex - yes. Intersecting "diagonals" be allowed - yes. 2nd UPD It is task for ...
0
votes
2answers
23 views

Right angled triangle log

If $a,b$ and $c$($c$ is the hypotenuse) are sides of a right triangle then prove $$(\log_{c+b}a)+(\log_{c-b}a)=2(\log_{c+b} a )\cdot(\log_{c-b}a)$$ The bases are different so can't quite figure out ...
1
vote
4answers
38 views

Calculate sides of right triangle with hypotenuse and area or perimeter

I'm trying to find if it is possible to find the lengths of the base and height of a right triangle with only the hypotenuse and the area (or the perimeter) of the triangle. I would have just figured ...