For questions about properties and applications of triangles

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3answers
84 views

Ratio of side length of triangle?

In triangle ABC, we choose a point D at AB such that the length of AD=1/2 AB, and point E at AC such that AE=3EC. F is intersection point of CD and BE. What is the ratio of CF/FD and BF/FE?
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1answer
835 views

Calculate Triangle Ground using Height and Top Angle

Is it possible to calculate the ground of a triangle only using the height and top angle. Click here to see a poorly draw sketch of what I'm trying to calculate. So is it possible and how, to ...
8
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4answers
239 views

equilateral triangle; $3(a^4 + b^4 + c^4 + d^4) = (a^2 + b^2 + c^2 + d^2)^2.$

In equilateral triangle ABC of side length d, if P is an internal point with PA = a, PB = b, and PC = c, the following pleasingly symmetrical relationship holds: $3(a^4 + b^4 + c^4 + d^4) = (a^2 + b^2 ...
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2answers
76 views

Is the orthocenter and incenter of a triangle the same point?

Although the orthoceneter and the incenter of a triangle are technically different things: The point in which the three altitudes of a triangle meet is called the orthocenter of the triangle. ...
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1answer
22 views

How do I find out the coordinates, interpolating across an angled line?

Suppose I know the coordinates of $A$ and $B$. The angle $X$ does not mean the total angle between the red lines, but rather how far along the angle that the purple line is. What is the easiest way ...
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1answer
123 views

portion of areas of two triangle

let us consider following picture we are given that this two line is parallel and also $AC=1/3 * AD$,we should find portion of areas of $ABC$ and $BCD$,now because $AB$ is one third of $AD$, ...
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1answer
714 views

A Question related to triangle and centroid .

The following is a geometry question I can't seem to get. "Consider an acute angle △ABC. Points D, E, F are mid points of sides BC, CA and AB respectively. G is the centroid of △ABC. Area of △AFG = ...
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3answers
313 views

Geometry problem on circles from a competition

Triangle $\triangle ABC$ is an equilateral triangle whose side is $16$. A circle meets the sides of the triangle at $6$ points: it intersects $AC$ at $G$ and $F$ and $|AG|=2$, $|GF|=13$, $|FC|=1$. ...
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2answers
127 views

Pythagoras Theorem in Triangles

The question is: In a triangle $\triangle ABC$, angle $\angle B = 90^\circ$ and $M$ is the mid-point of $BC$. Prove that $|AC|^2 = |AM|^2 + 3|BM|^2$. Please help me. I have tried various ways ...
0
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1answer
910 views

Find coordinates of vertex in right triangle

I have a right triangle with known points $A(x_1,y_1), B(x_2,y_2)$ and known cathetus $AC$ and $BA$. I need to find the coordinates of point $C$.
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3answers
1k views

Compare the sum of the squares of the median of a triangle to the sum of the squares of sides

You have to compare the sum of the squares of the median of a triangle to the sum of the squares of sides?
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1answer
264 views

Get legs length from right angle and hypotenuse

Here I have a 2 points. $A$ (lat,lng) and $B$ (lat,lng), this two point is hypotenuse of right triangle. How I can get legs length if I know angle, hypotenuse and these points?
3
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3answers
86 views

Sides of isosceles triangle

I have an isosceles triangle; the vertex angle and the base length are known (I think the base angles can be figured from this). How do I calculate the leg length?
3
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2answers
245 views

Calculating position/distance of point on arc of circle

I'm having a hard time trying to wrap my head around this problem. Imagine a line of length $A+B$ with center $C$, with a circle with $d = A+B$ with center at $C$. Now imagine drawing a line at ...
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2answers
101 views

Geometry Problem with isobarycenter and isoceles triangle

$XYZ$ a triangle with $XY=YZ.$ $D$ middle of $XY,$ $G$ isobarycenter of $XYZ.$ a circle $O,$ with center $D, XY$ are on $O.$ a circle $O',$ with center $G,$ $X$ and $Z$ are on $O'.$ 1/the ...
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1answer
211 views

What is the relation among sides of triangle in oval (ellipse)

if longest side of triangle is the longest diameter of oval, the rest point is located on the side of oval, you can vary it to change the triangle and except the longest side, set one of side of ...
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3answers
33 views

triangle row count from total points $x = \frac{n(n + 1)}2$

I'm trying to find the row count for triangle inputting the total number of points. I've found this, where $x$ is the total points, and $n$ is the rows. I'm having trouble solving it for $n$ $x = ...
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1answer
104 views

Help reducing the following expression involving Heron's formula for the area of a triangle.

Let $(ABC) = \sqrt{s \cdot (s - a) \cdot (s - b) \cdot (s - c).} $ This is Heron's formula for $(ABC),$ the area of $\Delta ABC,$ with sides $a, b, c,$ using $s = \frac{a + b + c}{2},$ the ...
1
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1answer
148 views

Triangle inequality for an obtuse triangle

$\alpha < 45^\circ$, how to show that 1) $|AB+AC|>|DB+DC|$? 2) $|AB+AC|>|DB+DC+DA|$?
41
votes
14answers
6k views

Do two right triangles with the same long hypotenuse have the same area?

I watched computer monitors and I asked myself, do two monitors with the same display diagonal have the same display area? I managed to find out that the answer is yes, if two right triangles with ...
0
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1answer
68 views

Use of triangle inequality for 2 triangles

In what angles of $\hat a, \hat b, \hat c, \hat d$ below conditions hold 1) $|AC+AD|>|BC+BD|$ or 1) $|AC+AD|<|BC+BD|$
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2answers
131 views

Calculate angle in triangle having 2 points and two lines

I have 2 points $B$ and $P$ and need to calculate angle $\alpha$ (maybe also I will need point $C$ and $E$) How can I do this. I know that I can calculate point $D$ it's $(\frac{1}{2}(x_P-x_B), ...
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3answers
447 views

How to be good at angles and trigonometry

I am Computer Science Engineer and loved algebra side of Mathematics. But when it comes to trigonometry and angles and triangles, I do not understand anything since college time. And till now also ...
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2answers
380 views

Properties of Triangle - Trigo Problem : In $\triangle $ABC prove that $a\cos(C+\theta) +c\cos(A-\theta) = b\cos\theta$

Problem : In $\triangle $ABC prove that $a\cos(C+\theta) +\cos(A-\theta) = b\cos\theta$ My approach : Using $\cos(A+B) =\cos A\cos B -\sin A\sin B and \cos(A-B) = \cos A\cos B +\sin A\sin B$, we ...
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1answer
69 views

Triangle of Multinomial Coefficients

What is the "Triangle Of Multinomial Coefficients" seen here: http://oeis.org/A036038 (OEIS: A036038) I can see that the diagonals of this triangle are just factorials... for example the last number ...
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vote
2answers
790 views

word problem about right-angle triangle

An observer who is standing $47$ m from a building, measures the angle of elevation of the top of the building as $17°.$ If the observers eye is $167$ cm from the ground, what is the height of the ...
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2answers
119 views

Fitting circle into an angle

I've been struggling with this for quite some time now, anyone could help me perhaps with this? Given an angle of an arbitrary degrees, and a circle with radius r. And imagine I would try to push the ...
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3answers
152 views

Nature of a triangle with vertices $z_1, z_2$ and $-1$ such that $|z_1|=|z_2|=1=z_1+z_2$ [closed]

If $z_1$ and $z_2$ are distinct complex number such that $|z_1|=|z_2|=1$ and $z_1+z_2=1$, then the triangle in the complex plane with $z_1,z_2$ and $-1$ as vertices must be: equilateral. right ...
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1answer
169 views

Altitudes Ratio

If h, h', h'' denote the lengths of the three altitudes of a triangle, which of the following ratios never occurs as the ratio h: h': h''? ...
2
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1answer
72 views

find parameter for maximize area

suppose that we have Cartesian coordinate system.and suppose that we have three point which depend on parameter $t$,where t belongs to $(0,1)$;points are $A(cos(3-t),sin(3-t))$ $B(cos(t),sin(t))$ ...
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2answers
99 views

find angle in triangle

Let us consider problem number 21 in the following link http://www.naec.ge/images/doc/EXAMS/math_2013_ver_1_web.pdf It is from georgian national exam, it is written (ამოცანა 21), where word ...
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4answers
170 views

Where does $\sin 3° =3\sin 1° -4 \sin^3 1°$ come from?

Wikipedia makes the claim: "Though a complex task, the analytical expression of $\sin 1°$ can be obtained by analytically solving the cubic equation $\sin 3° =3\sin 1° -4 \sin^3 1°$ from whose ...
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2answers
230 views

$x \sin x=2$ why is my proof that there no solutions wrong?

$\frac 12 x \sin x=1$ . Let's look at a right triangle with base $x$ and altitude $\sin x$ . Then our equation is for the area of this triangle. Let the sides of the triangle be $a=x$ , $b=\sqrt ...
0
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1answer
48 views

Modification of the triangle inequality

We know from the triangle inequality that $X+Y \geq Z$, My question is under what conditions of $a,b,c$ (acute, obtuse or right angle) that $Z >X $ and $Z \geq Y $
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votes
2answers
102 views

How can we prove that this triangle is Equilateral Triangle?

This is a problem which was sent to me by a friend , but i couldn't solve it , in particular , i don't have ideas for that . I hope you can help by hints or any thing . Here is the problem in the ...
2
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1answer
562 views

Move Point A along a line

Sorry, can't post images if my rep is below 10, and can't post more than 2 links. I removed the http section so it won't count as a link. I hope this isn't against forum rules, I'm not hurting anyone. ...
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2answers
343 views

Split a triangle into two right triangles

Lets assume I have a triangle $(p0, p1, p2)$ with $(p1 - p0)$ the longest edge. I am looking to find the point $q$ on the edge $(p1 - p0)$ such that $dot(p2 - q, p1 - p0) = 0$. That is to say; the ...
0
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1answer
87 views

Get Normal of a 3D point.

I have set of points. I created strip triangles using these points. Now I need to calculate normal. What I thought that for each triangle there should be a normal. But function I am using says that ...
3
votes
4answers
83 views

Limit on the expression containing sides of a triangle

To find the bounds of the expression $\frac{(a+b+c)^2}{ab+bc+ca}$, when a ,b, c are the sides of the triangle. I could disintegrate the given expression as $$\dfrac{a^2+b^2+c^2}{ab+bc+ca} + 2$$ and ...
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5answers
83 views

How to I find the length of a side on a triangle?

how do I find line AB in this if ac is 6cm, and bc is 14cm? angle A is 59*, c is 55*, and C is 66*. (not to scale) thanks in advance
2
votes
1answer
3k views

What's the ratio of triangles made by diagonals of a trapezoid/trapezium?

In the above image, what will be the ratio of areas of triangle $A$ and $B$? From Googling, I've found that: $\operatorname{Ar}(A) = \dfrac{a^2h}{2(a+b)}$ and $\operatorname{Ar}(B) = ...
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1answer
78 views

Radius of in-circle as a function of the center

I am trying to find the radius of an in-circle in a random triangle as a function of the center of the circle. Let (x,y) in\R^2 be the center of a circle, r the radius then i need an expression of the ...
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1answer
89 views

Tangent of circumscribed circle

I found a solution online which it said : "It's easy noted that $AG.AE$ = $AD^2$ = $AF^2$ (Using tangent of circumscribed circle)" I found this not obvious at all. I know that $AD = AF$ but why it ...
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1answer
766 views

Zero “norm” properties

I have seen the claim that the l0-norm ($\|X\|_0$ = support(X)) is a pseudo-norm because it does not satisfy all properties of a norm. I thought it to be triangle inequality, but am not able to show ...
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2answers
292 views

Does this proof work to prove that the greatest area of a triangle inside a circle is when the triangle is equilateral?

Does this proof work to prove that the greatest area of a triangle inside a circle is when the triangle is equilateral? I gather it doesn't because most of the proofs I've seen use derivatives etc. If ...
0
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1answer
56 views

Trigonometry problem, using COS

Let's say two right angled triangles share a common hypotenuse which measures 10 in length and share an angle which measures $20^\circ$ in total. How do I work out the value of x (the side adjacent to ...
0
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0answers
123 views

Line Triangle Intersection Mathematics

I am following the math in the book Real Time Collision Detection by Christer Ericson. On pages 184 thru 188, he discusses how to test for an intersecting line against a triangle. I replicated the ...
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3answers
173 views

Right Triangle Trig

I need to find the measure of each angle indicated and round to the nearest tenth. I am given two sides 12 and 13 and one angle C which is 90 degrees. How do I figure this out?
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3answers
1k views

Triangle inscribed in circle, vertex at circle's center, solve for unknown angles.

$O$ is the center of the circle , $A$ and $B$ lie on the circle what are the possible values of $x$ and $y$ I found answers options , asked to mark one or more ...
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3answers
83 views

Find coordinates of vertex of equilateral triangle

$ABC$ is an equilateral triangle , $AC = 2 $ What is the value of $p$ and $q$ ?