For questions about properties and applications of triangles

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1answer
18 views

Coordinates along lines in a Triangle

I've just lumbered myself with a bit of a maths problem. I have the triangle below Its 3 points are at these coordinates - $(-4.2,0),\,(0, 2.7),\,(5, 0)$. I know all of my coordinates along the ...
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3answers
422 views

Knowing the length of two sides of a triangle and the angle bisector in between , find the length of one of the altitude.

In $\triangle ABC$, $AB = 6, AC = 8$ and internal angle bisector $AD = 6$ such that $D$ lies on segment $ BC$. Compute the length of altitude $CF$ where $F$ is a point on line $AB$. For calculating ...
12
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3answers
5k views

Finding an angle within an 80-80-20 isosceles triangle

The following is a geometry puzzle from a math school book. Even though it has been a long time since I finished school, I remember this puzzle quite well, and I don't have a nice solution to it. So ...
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0answers
10 views

How calculate the area of a triangle inside a cuboid?

I have a large (order 10^7) collection of triangles in 3D space. I also have a cuboidal mesh also of order 10^7. For each triangle I need to calculate the area of that triangle which is inside any of ...
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3answers
4k views

How to find the type of triangle when given the ratio of it's sides?

Q.The sides of a triangle are in ratio 4 : 6 : 7, then the triangle is: (A) acute angled (B) obtuse angled (C) right angled (D) impossible It's definitely not (C) right-angled ...
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0answers
48 views

Isoperimetric hexagon and triangle ; comparing their areas. [on hold]

A regular hexagon ( all sides of equal length and all angles equal ) and an equilateral triangle is equal circumference. What percent larger is the largest area ??
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1answer
403 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''? ...
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1answer
266 views

Right triangle on an ellipse, find the area

Beginning note: Please wait until the animations load. The loading might take some time depending on your internet connection. Secondly, the title and the content of the question might not be well ...
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1answer
35 views

Is proof of Pythagoras Theorem using Similarity circular?

Please see this link. (hope it doesn't rot) Is this proof circular? I think similarity is proved by basic laws of trigonometry, especially Pythagoras theorem. When I search for proof of Similarity, ...
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1answer
24 views

Maximum area of a triangle when perimeter is fixed.

I can't solve the following problem: Show that amongst all triangles with perimeter $3p,$ the equilateral triangle with side $p$ has the largest area. Further show that $9p^2\ge 12\sqrt{3}\Delta.$ ...
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5answers
14k views

How can I find the lenght of the third side of any triangle

I will know the length of two sides of any triangle that I use, but I will not know any of the angles. I know how to find the length of the third side if I knew the angle where I am sitting, but how ...
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4answers
46 views

Is this a correct way to solve this high school coordinate geometry question?

Here's the question: Given point $A$: $(-3;-1)$ Given point $B$: $(3;7)$ Given point $Z$: $(x;0)$ Find the $x$ coordinate of point $Z$ so that the angle of view of AB segment is $90$ ...
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1answer
50 views

Sine law and circumscribed circle

How is $\frac{a}{\sin(A)}=2R$ (where $R$ is the radius) derived?
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2answers
59 views

How does the way we define cos or tan have anything to do with degrees of the angle?

So sine of angle $A$ is just a ratio. It is the ratio of the length of the opposite or perpendicular of angle $A$ and the hypotenuse. Cosine of angle $A$ is also just a ratio. It is the ratio of the ...
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1answer
35 views

Generic formula for third point of triangle knowing the other two points and all the side lengths

My question is similar to this one, but the solution provided makes use of some 'properties' that will not be true for all triangles. For example, if point A is not in the origin, or point B is not in ...
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2answers
35 views

Find angle of a right triangle.

Ok, so this question is from a practice exam. Looks very simple and basic, but I'm not very good at math, so I'm having trouble setting up the problem. One acute angle of a right triangle is not ...
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0answers
24 views

Angles and How they Correspond to Sides of a Triangle

I have done some Googling but am not sure what question I need to ask. I came here instead. I am at a 9th grade math level (Geometry) and working on a problem that is asking me to find x and y based ...
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0answers
29 views

Why we name one side as the perpendicular of an angle but does not actually define it?

If I have a right angled triange: $\qquad \qquad \qquad \qquad$ I was wondering why we name the sides like this? The base of $A$ kind of make sense. But the perpendicular of $A$ what relation does it ...
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0answers
19 views

Construction of a triangle using symmetry

I need to construct a triangle $\Delta \textrm{ABC}$ knowing that $t_a = AS$, $|AS| = 6\, cm$, $|\measuredangle \textrm{BCA}| = 30°$ and $|AB| = 5.5 \,cm$. I've been told that it's possible to do it ...
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1answer
24 views

Find altitude of equilateral triangle given inscribed circle dimensions and position

I've found myself trying to solve this for my Geometry class where we have to model a basic piece of architecture and find its volume and surface area (very basic). But the structure I chose requires ...
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3answers
2k views

Find perimeter and angle of triangle using three 3d vectors .

Given the following, three vectors: $$\vec{a} = 3\mathrm{i} - 2\mathrm{j} + 5\mathrm{k}\\\vec{b} = \mathrm{i} - 6\mathrm{j} + 6\mathrm{k}\\\vec{c} = 2\mathrm{i} + 3\mathrm{j} - \mathrm{k},\\$$ find ...
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1answer
30 views

Given a triangle $ABC$, Find a point $P$ such that $PA:PB:PC=1:2:3.$ [closed]

"Given a triangle $ABC$, Find a point $P$ such that $PA:PB:PC=1:2:3.$ I found this on a Olympiad book, and I was unable to solve it. Any help will be appreciated.
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1answer
48 views

Question about area and triangle

Problem: Consider the following diagram. in $\triangle$ABC: Areas: $\triangle$AOM = a $\triangle$POC = b $\triangle$NOC = c $\triangle$BON = d. Find the area of $\triangle$MOB and ...
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2answers
47 views

Prove that length of three bisectors determine triangle.

All of us know that length of 3 bisectors determine triangle. But actually all proofs that I heard are sufficient large. So I'm interested in short and smart proof. Any ideas?
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1answer
19 views

Euclidean Geometry Equilateral Triangle Problem

ABC is a equilateral triangle with vertex A fixed and B moving in a given straight line. Find the locus of C. Though it is clear that being an equilateral triangle, the size of the triangle must ...
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1answer
11 views

Sum of the length of the perpendiculars - property of equliateral triangles

Consider an equilateral triangle ABC P is a point on AB, Q is a point on BC Suppose we draw perpendiculars from P to other sides. Let s1 be the sum of the length of these ...
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2answers
464 views

For which $N$ is it possible to alter one side of an equilateral triangle of side length $N$ to get another triangle of integer side lengths, …?

This question is "inspired" by the Rupsa and Equilateral Triangle problem from Code Chef's "October Challenge 2015". The deadline of 12 October 2015 has passed. Given an equilateral triangle having ...
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1answer
52 views

In a triangle $ABC$ with side $AB=AC$ and $\angle BAC=20 ^\circ $. $D $ is a point on side $AC$ and $BC = AD$. Find $ \angle DBC$

Problem : In a triangle $ABC$ with side $AB=AC$ and $\angle BAC=20 ^\circ $. $D $ is a point on side $AC$ and $BC = AD$. Find $ \angle DBC$ Solution: $AB =AC$ So $ \angle ACB = \angle ABC$ $ ...
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1answer
30 views

Solve using Law of Cosines or Law of Sines

I'm trying to solve these sets of problems please. Determine the number of triangles with the given parts and solve each triangle (if possible). $\alpha=39.6^\circ,c=18.4,a=3.7$ ...
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1answer
431 views

Finding Y coordinate of third triangle point when X coordinate and two other points are already known

Suppose you know the coordinates for points A and B of a triangle. We can refer to those coordinates as (Ay,Ax) and (By,Bx). Also, suppose you know the X coordinate for point C (Cx) but do not know ...
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1answer
40 views

How can I find ratio between area of triangle and area of quadrilateral?

I have a parallelogram $ABCD$. $E$ is center of $AD$. $O$ is center of $AC$ and center of $DB$. $F$ is the intersection point between $CE$ and $DO$. Point $G$ is the intersection between $EO$ and ...
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1answer
34 views

Distance from Chicago to New York

An airplane flies $520$ miles from Chicago to Virginia. Then it turns $45$ degrees to face New York and flies $630$ miles to New York. What is the distance from Chicago to New York? Given the $45$ ...
2
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1answer
36 views

Does three medians determine a triangle?

If given three medians, is there only one triangle that has these three medians? How do I prove that?
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2answers
59 views

Triangle angle question [closed]

I need help about a triangle angle question.
0
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1answer
53 views

Why aren't area of triangle not same when calculated by different methods in this case

I came across a question today. Two mutually perpendicular straight lines through the origin forms an isosceles triangle with the line $2x + y = 5$. Then the area of the triangle is ? I know ...
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1answer
821 views

How to solve bearing of oblique triangle

I'm having a hard time finding the solution of the bearing given in our example. Our Example: Suppose there's a triangle with points named A,B, and C. Point A is named Bacoor. Point B is named San ...
0
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1answer
19 views

Points $A,B,C$ are $z_1,z_2$ and $(1-i)z_1+iz_2$ . Then find nature of triangle $ABC$

The points $A,B,C$ represent the complex number $z_1,z_2$ and $(1-i)z_1+iz_2$ respectively on the complex plane. Then triangle $ABC$ is: $(A)$ Isosceles but not right angled $(B)$ Right angled but ...
0
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1answer
510 views

How to find heading angle to an object who's x,y coordinates are known?

Scenario: I have a map with a marked location on it. I know my x,y coordinates on the map (top left corner is 0,0), my distance from that marked location, my heading angle relative to true north (0 is ...
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0answers
27 views

Area of a triangle on an Argand diagram

I am working on two problems: 1) Find three distinct roots of the equation $8z^3 + 27 = 0$ I solved this and ended up with \begin{align*}z_1 &= \frac32 \left( \cos (\pi/3) + ...
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6answers
39 views

How to find the area of a triangle with two equations?

So I was given the following problem : ABC is a right angled triangle with the sides $a,b,c$ . Find the area of this triangle, given that $$a+b+c = 22$$ $$a^2+b^2+c^2 = 200$$ I've tried to do a lot ...
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1answer
22 views

Defining a region in $\mathbb{R}^2$

I was trying to do this exercise but my answer doesn't match with the solution and I'm wondering why: Consider the coordinates transformation defined by $x=2u+v$ and $y=u^2-v$. Being $T$ the ...
0
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1answer
16 views

Right Triangle Angle problem

So I know that this can be easy, but I found it a bit difficult so maybe someone can just explain or give a hint to me... I cant post image due to no reputation (this is my first post) so theres the ...
2
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2answers
45 views

How to parameterize the interior of a triangle

I would like to know how to parameterize a triangle over $[0,1] \times [0,1]$. I actually only care that the mapping is surjective but a bijection is always nice I suppose. I found this in which an ...
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0answers
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Similar Triangle dissections

Andrzej Zak found that a triangle with sides based on powers of the root $d^6-d^2-1=0$, $(d=1.15096...)$ that can replicate itself with 6 differently sized copies. The numbers are powers of $d$. The ...
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0answers
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Get location / position of an object via 2 cameras

Best In the following image, you can view the setup of my problem. In general, i've 2 cameras which have a view-angle of 48° and 64°. Secondly, I know the position of my camera's (which means i can ...
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6answers
3k views

Why is not possible to draw this triangle?

Why is it not possible to draw triangle $DEF$ with $EF=5.5cm$,$\angle E=75^0$ and $DE-DF=1.5cm$?(I used this method for ...
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3answers
167 views

Similar triangle proof in parallelogram

Can anyone help me with this task. From the top of a parallelogram $ABCD$ lowered the vertical $AM$ and $AN$ on the lines BC and CD . Prove that triangles $\triangle ABC$ and $\triangle AMN$ similar ...
4
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1answer
256 views

History of incenter and Euler line

It is easy to see that if a triangle is isosceles, then its incenter lies on its Euler line. Who first proved the converse of this result and what technique was used? (See the post "The incenter and ...
0
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1answer
24 views

For any point inside a triangle

Let $P$ be an interior point of the triangle $\triangle ABC$. Assume that $AP$, $BP$ and $CP$ meet the opposite sides $BC$, $CA$ and $AB$ at $D$, $E$ and $F$, respectively. Show that $\frac{AF}{FB} ...
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0answers
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An interesting geometry problem with angle bisectors and tangent

I have found the following problem: There is an acute $\triangle ABC$. Denote its circumcircle as $\omega$. The angle bisector of $\angle BAC$ intersects $BC$ and $\omega$ in points respectively $A_1$ ...