For questions about properties and applications of triangles

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2
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1answer
21 views

Rotation of Rectangle Based on a Triangle in 3D Space

I am trying to transform a rectangle centered at the origin and dimensions of $(\| P_2 - P_1 \|, 0, \| \mathbf{V_P} \|)$ to a triangle in 3D space with points $P_0$, $P_1$, and $P_2$ where ...
0
votes
2answers
94 views

If $\sin(A) = \cos(A)$ find $2 \tan^2 A - 2 \sec^2 A + 5$ [closed]

This is my first try to trigonometry, I have solved 100s of questions but this one always comes incorrect! Can anyone help me? Question: If $\sin A = \cos A$, find the value of: $2 \tan^2 A - 2 ...
4
votes
3answers
64 views

Proving $\cot { A+\cot { B+\cot { C=\frac { { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 } }{ 4K } } } } $ [closed]

For any acute $\triangle ABC$, prove that $\cot { A+\cot { B+\cot { C=\frac { { a }^{ 2 }+{ b }^{ 2 }+{ c }^{ 2 } }{ 4K } } } } $, where $K$ is the area of $\triangle ABC$. Unfortunately I'm ...
1
vote
1answer
57 views

Finding and proving similar triangles

ABC is a triangle with AB shorter than side AC. The angle bisector of ∠A intersect BC at D. Given that point E is on the median that's drawn from A, so that BE⊥AD, how do I show that DE||AB? I tried ...
0
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3answers
84 views

How to plot a triangle, given three side lengths?

I want to plot a triangle, given side lengths $a$, $b$, and $c$. I can plot point $A$—opposite side $a$—at the origin $(A_x = 0,\ A_y = 0)$. I can plot point $B$—opposite side $b$—along the $x$-axis ...
3
votes
1answer
130 views

Olympiad Trigonometric Inequality

Let $R$ and $r$ be the circumradius and inradius of $\triangle ABC$. Prove that $$\frac { \cos { A } }{ { \sin }^{ 2 }A } +\frac { \cos { B } }{ { \sin }^{ 2 }B } +\frac { \cos { C } }{ { ...
1
vote
0answers
46 views

Determine third point of Right Triangle when two points and all sides are known and $A\hat BC=90$

I have two points and all sides of right triangle I need find A point \begin{gather*} |AB| = 1 \\ |BC| = 1 \\ |AC| = \sqrt{1^2 + 1^2} = \sqrt2 \\ A(?,?) \\ B(0,0) \\ C(1,0) \\ \\ |AB| = 1 \\ |BC| = ...
4
votes
1answer
29 views

How to triangulate from a Voronoï diagram?

I computed a Voronoï diagram from a set of point (with Boost.polygon). I try to find a Delaunay triangulation, connecting each cell center for each Voronoï edge, but I miss some edges. In the ...
0
votes
2answers
34 views

Finding side of a triangle

$ST$ is the perpendicular bisector of $PR$ and $SP$ is the angle bisector of $\angle QPR$. If $QS=9cm$ and $SR=7cm$ then $PR$ = $x/y$ where $x$, $y$ are coprimes. $x$ + $y$ = ? I tried to use the ...
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3answers
49 views

Side of a triangle

In the figure, $AB=10\sqrt2$, $AC=11\sqrt2$ and $BC=12\sqrt2$.$DE$ and $BC$ are parallel and divides the triangle into two parts with equal area. What is the length of the line DE? ...
0
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2answers
47 views

Determine the unknown angle

For this question I'm a bit confused and don't know where to start by solving it, any guidance is appreciated.
2
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3answers
30 views

Determine the unknown side lengths

Rounded to nearest tenth solving for $y$: tan = opposite / adjacent 12tan(53°) = 15.9 cm solving for $z$: cos = adjacent / hypotenuse 12cos(53°) = 9.6 cm Am I correct? Also, the thing that ...
0
votes
2answers
27 views

Finding 3rd Point of Isosceles Triangle

Im trying to find a way to calculate the position of the one of the base points of an isocicles triangle if I know the positions of the other two points, the angle measures, and the side lengths. It ...
4
votes
1answer
99 views

Prove the triangle is equilateral given that a quadrilateral related to its circumcircle is a kite

Let $\triangle ABC$ be a triangle. Let $Γ$ be its circumcircle, and let $I$ be it’s incenter. Let the internal angle bisectors of $∠A,∠B,∠C$ meet $Γ$ in $A',B',C'$ respectively. Let $B'C'$ intersect ...
1
vote
1answer
35 views

A triangular piece of land has one side measuring 2ft.

A triangular piece of land has one side measuring 2ft. The land is to be divided into 2 equal areas by a dividing line parallel to the given side. What is the length of the dividing line? so far ...
0
votes
1answer
50 views

At what angle does the stone have to be hit? [duplicate]

What I have so far: 11 inches = 0.916667 feet Let a represent θ tan a = 0.916667 / 87 = 0.010536402 tan^-1(0.010536402) = 0.6036... rounded to 0.6 degrees. Is this correct?
0
votes
1answer
73 views

What is the value of x in this diagram?

So I'm pretty familiar with SOH-CAH-TOA but this question in particular looks a bit different and I'm not sure how to go about it. Thanks in advance!
0
votes
3answers
47 views

How many triangles with ∠ABC = 90° and AB= 20 exist such that all sides have integer lengths? (A) 1 (B) 2 (C) 3 (D) 4 (E) 6

How many triangles with $\angle ABC = 90°$ and $\overline{AB}= 20$ exist such that all sides have integer lengths? $(A)\; 1 ,\;\;(B) \;2 ,\;\;(C)\; 3 ,\;\;(D)\; 4 ,\;\;(E)\; 6$ I know the answer ...
2
votes
1answer
29 views

How do I calculate the distance from point A from point B?

I've got this drawing of a circle, and I'd like to know how I can calculate the distance between point A to point B in a straight line. I already have: Radius: 100 Arc length: 78.5 ...
2
votes
2answers
73 views

Is this a valid proof that the sum of the angles in a triangle is $180^\circ$?

I think I accidentally found a proof of the famous theorem that the sum of the angles of a triangle add up to $180 ^\circ$, but am not sure if it is correct. Here it is: It can be proved that the ...
1
vote
2answers
35 views

What are the unknown angles in the diagram below?

So I used the Pythagorean theorem to find the missing leg first. $$a^2 + b^2 = c^2$$ $$a^2 + 6^2 = 10^2$$ $$a^2 + 36 = 100$$ $$100 - 36 = 64$$ $$\sqrt{64} = 8$$ Now I'm just lost from here. It ...
0
votes
1answer
48 views

Find the ratio of the radii

Euclid Contest April 2015 Problem 8B I cannot type it as it has a diagram along with it, which might mess up my interpretation. This was a tough problem, I cannot solve it completely. HINTS ...
1
vote
1answer
36 views

Given coordinates find triangle and circle intersections

For example we have a circle and triangle. We need to check if at given $(m, n)$ coordinate triangle is intersecting with circle (area). Circle center is fixed at $(100, 100)$ with radius $R = 50$. ...
1
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2answers
32 views

Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.

The question is as follows if $ABC$ is a triangle, with $AD$ as the internal angle bisector of $\angle A$ with $D$ at $BC$ and $B^{'}, C^{'}$ are reflection of points $B$ and $C$ in $AD$. Show that ...
1
vote
2answers
42 views

Reflection through bisector of angle $\angle A$

Let ABC be a triangle. Let B' and C' denote respectively the reflection of B and C in the internal angle bisector of $\angle A$, Show that the triangle ABC and AB'C' have the same in centre? What ...
2
votes
1answer
13 views

How to Prove Triangle Centers in Tetrahedra

How would you prove the existence of triangle centers in tetrahedra, for example, the incenter, circumcenter, or centroid?
0
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2answers
25 views

How to find triangle height if I know its area and angles

For example, there is a triangle $ABC$ with angles $\alpha = 45^\circ, \beta = 120 ^\circ, \gamma = 15^\circ$. $\text{Area } S = 15$. How to find all three heights of the triangle?
0
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2answers
24 views

Find the angle of depression given the following two right triangle?

A person in a control tower is looking at an airplane that is 78 yards away from the base of the tower on the runaway. If the person is 27 yards in the air, find the angle of depression from the tower ...
1
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2answers
76 views

Area of a Triangle Inside a Circle?

I have a circle of radius $r$ and a triangle inside that circle. Specifically, if you have the triangle $\triangle ABC$ inside a circle with only the one side $AB$ and an angle $\angle \text{B}$ ...
1
vote
1answer
20 views

Do the properties of a pedal triangle hold good when the triangle on which the pedal triangle is constructed, an obtuse an triangle?

For Example, Can we assume that the incentre of a pedal triangle is the orthocentre of the triangle on which the pedal triangle is constructed in all cases?
1
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1answer
57 views

Calculating the area of a triangle assuming you don't know Heron's formula

I was wondering - let's say you know the lengths of the sides of a triangle and you want to calculate its area. This could be performed very easily if you know Heron's formula but... What if you ...
1
vote
1answer
42 views

Can the Pythagoras theorem be applied to other polygons apart from squares in relation to right angular triangles?

Is the sum of area of any regular polygon made in the two sides of a right angular triangle equal to the area of the same polygon made at the hypotenuse? If so how to prove it? The area was equal to ...
0
votes
1answer
53 views

Finding the third vertex of a isosceles triangle given the vertices of the base and knowing that the medians are perpendicular

Full problem: The points A(0, c) and B(c, 0) are the vetrices of the base of an isosceles triangle. In addition, the medians AD and BE are perpendicular to each other. What are the coordinates of the ...
0
votes
3answers
56 views

Minimum Value in a traingle

In any triangle, what is minimum possible value of $\frac{r_1 r_2 r_3}{r^3}$? I reduced its value to $ (s^4)/(Area^2) $, But I don't know how to proceed now? Where $ r_1 r_2 r_3 $ are exradii, r is ...
0
votes
0answers
57 views

Proof for Pappus's Centroid Theorem with basic geometry?

How to prove Pappus's Centroid theorem about volume for a triangle rotated around an external axe? The theorem says that the volume V of a solid of revolution generated by rotating a plane figure F ...
0
votes
2answers
54 views

How to solve this inequality involving trig functions: $\frac{\sin B + \sin C}{2}\leq \sin\left(\frac{B+C}{2}\right)$?

Source - Larsen 1.3.12 Problem: Prove using $y=\sin(x)$ graph, for $A,B,C$ as angles of triangle, that: $$\frac{\sin B + \sin C}{2}\leq \sin\left(\frac{B+C}{2}\right)$$ Attempt: (without ...
2
votes
1answer
77 views

Finding the angles of $\triangle ABC$

In a $\triangle ABC$, from vertex $C$, the median to $AB$, the angle bisector of $\angle BCA$ and the perpendicular to $AB$ divides angle $\angle BCA$ into four equal parts. The task is to compute ...
0
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1answer
48 views

Triangle Formula for alternative Points

With this formula I tried to calculate the third point in a triangle: http://math.stackexchange.com/a/1553606/126977 I know the length between the two point points and the angles at this corners: ...
0
votes
1answer
45 views

How to find a point in a Right Triangle given 2 known points, all sides, all interior angles

This triangle is not parallel or vertical, it's in a 2d plane. Distance formula gave me very troubling results, looking to use SOH CAH TOA, particularly a simple method and not a complex method of ...
2
votes
1answer
88 views

Proof involving Ramsey numbers

$S$ is a set of R(m,m;3) points in the plane in which no 3 points are collinear. I am trying to prove that $S$ contains $m$ points that form a convex $m$-gon. I have tried using similar logic to the ...
0
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1answer
21 views

centroid of a cone in comparison to the centroid of a triangle

If one has a triangle, the centroid is located 1/3 of its height from its longest edge, see: [triangle centroid][1], however for a cone it is instead located a ...
0
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2answers
81 views

Calculate Third Point of Triangle

I'm trying to calculate the third point of a triangle: I know two points, (2,3) and (5,2) and the angles at this sides, both of ...
0
votes
1answer
36 views

How do I get a point from two points using a right triangle?

In the image the triangle is made up of 3 points, 2 of which are found, the third one is missing, not sure how to get this last point. [Need an Equation]
4
votes
1answer
44 views

Hexagon tesselations

A configuration is made of congruent regular hexagons,where each hexagon shares a side with another hexagon. What is the largest integer $k$, such that the figure cannot have $k$ vertices ? For ...
0
votes
1answer
26 views

Help solving this GCSE question on angles/parallel lines/isoscelesh

Problem: $ABC$ is an isosceles triangle with angle $\angle ABC=52^\circ$. $XY$ is parallel to $BC$. Work out the size of angle $\angle BAC$. Hi I need help solving this GCSE question under the ...
0
votes
1answer
34 views

Calculate the coordinates of the point P, knowing that A=(2,0) and OA=AB.

I have the following problem. In the figure, the circumference is tangent to the Y-axis in the point P, the point A has coordinates (2,0) and OA=AB. I am asked to calculate the coordinates of the ...
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3answers
32 views

Find the Coordinates of a Unkown Point of a Triangle

The situation is as follows: I am creating a game in this game I have a line($A$ to $B$) and a mouse position $C$. Now I want to calculate point $D$ on line $A$$B$. I know the coordinates of: $A$, ...
10
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5answers
311 views

Prove that $\angle FGH = \angle GDJ$

Let $FGH$ be a triangle with circumcircle $A$ and incircle $B$, the latter with touchpoint $J$ in side $GH$. Let $C$ be a circle tangent to sides $FG$ and $FH$ and to $A$, and let $D$ be the point ...
0
votes
2answers
70 views

How to find the length of the line segment of this following triangle?

Given: right triangle ABC with C as a right angle. Line DE is formed, such that ED is perpendicular to AB. D at AB and E at CB. If AC=AD= 8 cm and CE=DE, what is the length of BE? My ...
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votes
2answers
40 views

formula for calculating any angle of an isosceles triangle

This might be an easy question to ask, but for some reason I can not find the right formula to calculate one (does not matter which one) angle (red) of an isosceles triangle (green). Here is an ...