For questions about properties and applications of triangles

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2answers
348 views

Similarity involving Miquel's Theorem

Let $\Delta ABC$ be a triangle. If we place points $D,\ E,\ F$ arbitrarily on the sides $\overline{AB},\ \overline{BC}$ and $\overline{CA}$ respectively, then the circumcircles of the triangles ...
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3answers
965 views

How to calculate radius of flush arch between two intersecting lines?

I am trying to make a corner of a robot I am designing flush for aesthetic reasons as well as safety reasons but I'm not sure how to make the arch of the corner lay flush with the two lines that make ...
0
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1answer
2k views

How many triangles can be formed from N points on a circle?

I have a circle with N points on it, and I want to determine how many triangles can be formed using these points. How can I do this? Thanks! Andrew
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1answer
32 views

Need help developing the formula to calculate the length of the y axis of a right triangle with a curved side for any position on the x axis.

If a right triangle has one side that is 500, another side that is 208, and the last side with a radius of 705, what is the formula to determine the length of the intersection point (y) at any given ...
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2answers
224 views

What is the logic to calculate triangle-inequality-theorem

So I want to know is there any simple formula to get the result for the triangle-inequality-theorem I know what is the theorem but any formula rather than doing it the routine way of adding then ...
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0answers
41 views

Triangular exponentation logarithm and inverse

The generalized formula of triangular exponentation on real numbers field is $x ^ {\triangle y} = \frac {1} {y \cdot B (x, y)} = \frac {\Gamma(x + y)} {\Gamma(x) \cdot \Gamma(y + 1)} $ It's my ...
2
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2answers
101 views

Generating integral triangles with two equal sides

How can I generate all triangles which have integral sides and area, and exactly two of its three sides are equal? For example, a triangle with sides ${5,5,6}$ satisfies these terms.
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7answers
12k views

Geometry triangle question

In the figure below, AB=BC=CD. If the area of triangle CDE is 42, what is the area of triangle ADG? I think triangles are similar. Are there any properties of similar triangles regarding their area. ...
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2answers
145 views

Showing that $ 1<\sin\frac{\alpha}{2}+\sin\frac{\beta}{2}+\sin\frac{\gamma}{2}$

I would like to show that: $$ 1<\sin\frac{\alpha}{2}+\sin\frac{\beta}{2}+\sin\frac{\gamma}{2}$$ where $\alpha, \beta, \gamma$ are the angles of a triangle. I know that the inequality $$ ...
4
votes
4answers
96 views

How is this angle relation true?

Either I'm silly and I'm missing something very simple, or my text book is incorrect. I'm trying to verify a line in the text book which claims that sin(a) = s/r. I can't seem to prove this to myself ...
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0answers
231 views

pixels in a projection of a triangle in 3d space onto a 3d plane through a pinhole camera

I have a triangle in 3d space. The x and y components of its vertices make a 2d right isoceles triangle. I am projecting it through a pinhole onto a plane. The projected triangles on the plane are now ...
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1answer
460 views

Geometry Proving Isosceles Triangle

This question seems tricky and I frankly don't know how to start. I will be grateful if someone can provide a solution. We have a triangle $ABC$ and there is a point $F$ on $BC$ such that $AF$ ...
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3answers
4k views

Calculate coordinates of 3rd point (vertex) of a scalene triangle if angles and sides are known.

I am writing a program and I need to calculate the 3rd point of a triangle if the other two points, all sides and angles are known. ...
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3answers
7k views

How to determine if a 3D triangle given by points is a right triangle?

How do I figure out if a triangle is a right triangle in 3-D space if you are given three points: $P = (3, -2, -3)$, $Q = (7, 0, 1)$, $R = (1, 2, 1)$? I know that it is an isosceles triangle (two ...
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vote
2answers
319 views

2 Right triangles, which ratio is equal to 1?

Say you have a right triangle, you know the length of the 2 sides of the 90 degree corner (so you know everything, the hypotenuse and all 3 angles). Inside this triangle, you draw a line (not the ...
2
votes
1answer
2k views

How to calculate the rotation matrix between 2 3D triangles?

I need to calculate the rotation matrix and the translation vector between 2 given triangles in Euclidean space. This is really just a rotation and a translation, the lengths of sides of the triangle ...
2
votes
1answer
5k views

Trigonometry problem involving oblique triangle

How would I solve the following problem? A ship sails $15$ miles on a course $S40^\circ10'W$(south 40 degrees 10 minutes west) and then $21$ miles on a course $N28^\circ20'W$(north 28 degrees 20 ...
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vote
2answers
886 views

What is the number of triangles with integer sides, given the length of the longest side?

Suppose $a,b,c \in\mathbb N$, and the value of $c$ is known and fixed, while $a$ and $b$ are unknown and are both smaller than $c$. What is the total number of unique triangles possible with $a, b$ ...
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votes
2answers
158 views

Consider a triangle with sides, $3,4,5$, does $3^2+4^2=5^2$ hold for such a triangle.

Consider a triangle with sides, $3,4,5$, let the angle opposite the greatest side $5$ be $\theta$, does $3^2+4^2=5^2$ hold for such a triangle. Now consider a triangle with sides (1,1,$\sqrt{2}$), let ...
3
votes
1answer
431 views

Is this a norm? (triangle inequality for weighted maximum norm)

I've been trying to prove that the following is a norm, but wasn't successful. I also cannot find a counterexample. So help is greatly appreciated. Let $x \in \mathbb{R}^N, \ w_i \in \mathbb{R}_+,\ ...
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1answer
119 views

how to find(measure,calculate) the distance (height,length) of an object?

I am trying to develope code ,so i need a mathematics help to proceed,please help me to find distance of an object using trigonometry r any applicable maths without using any sensors r external ...
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5answers
578 views

Maximum area of a triangle

I have been attempting to solve the problem here which is: Given three concentric circles of radii 1, 2, and 3, respectively, find the maximum area of a triangle that has one vertex on each of ...
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1answer
223 views

Scalar product equals weighted sum of projection of the vectors onto the edges of a simplex

Given a triangle with the edges $e_1$, $e_2$, $e_3$, it seems (from numerical evidence) that there are coefficients $\alpha_i$ such that $$ u^Hv = \sum_{i=1}^3 \alpha_i \, (u^He_i)\, (e_i^H v) $$ ...
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2answers
1k views

Will this problem be solved using Thales theorem for triangles

I am stumped on the following question: In triangle ABC , AD=DB , DE is parallel to BC. The area of Triangle ABC is 40. What is the area of triangle ADE I know Thales theorem must be ...
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1answer
82 views

Possibilities of x in a right angle tringle

I am stumped on the following question: Which of the following could be the value of x in the diagram a)10 b)20 c)30 d)40 e)50 (Ans b and c) Any suggestions relating to solving this ...
2
votes
2answers
560 views

Height of triangle inside a parallelogram

I am stumped on the following question PQRS is a parallelogram and ST=TR. What is the ratio of area of triangle QST to the area of parallelogram (Ans 1:4) I need the height of the ...
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vote
2answers
564 views

Area of Triangle inside another Triangle

I am stumped on the following question: In the figure below $AD=4$ , $AB=3$ , and $CD=9$. What is the area of Triangle AEC? I need to solve this using trigonometric ratios however ...
2
votes
1answer
212 views

Trigonometric inequality for angles in triangle

Let $A, B, C$ be angles in a triangle. Is the following inequality $$4\cos A \le 1 + \cos\left(\frac{B-C}{2}\right)$$ true? I just assume it but don't have a proof. Thank you for your help.
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2answers
1k views

Deriving the formula for the radius of the circle inscribed in an equilateral triangle

I am trying to derive the formula for the radius of the circle inscribed in an equilateral triangle from scratch. Given $2*n$ = length of a side $H$ = the altitude of the triangle = $h + a$ ...
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4answers
4k views

Perimeter of Triangle inside a circle

If the circle has a radius of 4, what is the perimeter of the inscribed equilateral triangle? Answer: $12\sqrt{3}$
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3answers
716 views

Triangle Inside Circle

If the radius of the circle is equal to the length of the chord $AB$, what is the value of $x$? How would I solve this problem ?
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1answer
221 views

How to find the area of green region in terms of yellow, blue and red region in the following figure?

How to find the area of green region in terms of yellow, blue and red region in the following figure? The triangle is any random triangle and an arbitrary point $P$ is taken where all the colored ...
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votes
3answers
1k views

Why is the inradius of any triangle at most half its circumradius?

Is there any geometrically simple reason why the inradius of a triangle should be at most half its circumradius? I end up wanting the fact for this answer. I know of two proofs of this fact. Proof ...
3
votes
1answer
3k views

How many triangles with integral side lengths are possible, provided their perimeter is $36$ units?

How many triangles with integral side lengths are possible, provided their perimeter is $36$ units? My approach: Let the side lengths be $a, b, c$; now, $$a + b + c = 36$$ Now, $1 \leq a, b, c ...
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2answers
4k views

What is The 3rd side length of Isosceles Triangle

I've a isosceles triangle which length is $10\;\mathrm{cm}$ , $10\;\mathrm{cm}$ and $x$. If I want to make this triangle $120^\circ$ degree then what should be the $x$?
3
votes
3answers
562 views

Pythagorean Theorem for imaginary numbers

If we let one leg be real-valued and the other leg equal $bi$ then the Pythagorean Theorem changes to $a^2-b^2=c^2$ which results in some kooky numbers. For what reason does this not make sense? Does ...
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1answer
180 views

Irrational distances, rational area triangles

Given any positive integer $n\ge3$ how to show that there are $n$ distinct points in the plane such that 1- the distance between any two points is irrational number and 2- each set of three points ...
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2answers
170 views

Finding Height of a Triangle

I am having problem with the following question: From the triangle which is greater Area of the Triangle ABC or 27 Now how would I find the height of such a triangle.
3
votes
3answers
301 views

Deteriming an angle without Trig. ratios

I am trying to solve the current problem If O is the center of a circle with diameter 10 and the perimeter of AOB=16 then which is more x or 60 Now I know the triangle above is an ...
2
votes
2answers
8k views

Finding the area of triangle if length of medians are given

My question is: In triangle ABC ,length of median from vertex A is $13$ , length of median from vertex B is $14$ , length of median from vertex C is $15$. Compute the area of triangle ABC.
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votes
2answers
654 views

Finding relative coordinates in triangle

Known: $r$, coordinates of $A$, angle $BAC$=72° Task: find coordinates of B and C. So, I have 4 unknown parameters to compute, but only 3 equations. $r^2$=$(x_a-x_b)^2+(y_a-y_b)^2 $ $(2.49r)^2 = ...
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votes
2answers
655 views

Why is $d\theta/dx$ necessarily $\cos \theta$ in this physics problem? Or am I wrong?

I'm asking this on the math stack exchange because it seems that the key part of this physics problem I'm asking for help on is more related to the geometry of it than the physics of it. I'm ...
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1answer
368 views

divide triangle into ratio 1:2

I have a problem related to triangles. Please give me some hint to progress. Suppose we have the following coordinates $A(-2,3)$,$B(1,-1)$,$C(-1,-1)$. From point $A$, draw a line which divides ...
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1answer
413 views

Finding area of triangle

if the sides of the triangle are given by 20 cm, 30 cm, and 60 cm find the area of the triangle. I tried a long time. Apparently, Heron's formula does not seem to work $\sqrt{s(s-a)(s-b)(s-c)}$ ...
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3answers
4k views

Is it safe to assume that the altitude of a triangle always cuts the base in half

While solving different questions , I realized that whenever I constructed an altitude it always bisected the base in half. From what I deduced from Wikipedia is that this is only true if the triangle ...
0
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1answer
134 views

What does the negative in this anwer depict.

For the following question: Peter lives 12 miles west of school and Bill lives north of school.Peter finds the direct distance from his house to Bill is 6 miles shorter than the distance by ...
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1answer
182 views

Getting the angles of a triangle

I am having trouble with the following question In the following figure if PQ=QS and QR=RS and angle PRS is 100 degrees what is the measure of angle QPS (Ans = 20) Now here is how far ...
1
vote
1answer
666 views

Pythagorean theorem

We can make a square into four equal squares. Fine, if we want to make into five.. Then there is a problem. Please discuss, How to make five squares from a single square by using a Pythagorean ...
2
votes
2answers
261 views

Finding the smallest possible angles in a triangle

I am having difficulty solving this problem: In the given figure (x+y) is an integer greater than 110. What is the smallest possible values of (w+z) (ans is 111)? Any suggestion on how ...