For questions about properties and applications of triangles

learn more… | top users | synonyms

1
vote
2answers
41 views

Find the area of triangle, given an angle and the length of the segments cut by the projection of the incenter on the opposite side.

In a triangle $ABC$, one of the angles (say $\widehat{C}$) equals $60^\circ$. Given that the incircle touches the opposite side ($AB$) in a point that splits it in two segments having length $a$ ...
0
votes
1answer
15 views

***M>N*** Find the ratio of M to N and hence find two possilbe sets of lengths for the sides

Right Angled triangle with Long Side: M+N Side 1: M-N Side 2: M Im stuck on this question. Never done ratios in class with right angled triangles so I'm so confused. Some help would be appreciated
0
votes
1answer
21 views

What is the angle of b?

So first off, I know how to find the missing length of the leg of the triangle using the pythagorean theorem. $6^2 + b^2 = c^2$ $36 + b^2 = 100$ $100 - 36 = 64$ $\sqrt{64} = 8$. So angle angle ...
0
votes
2answers
35 views

What angle does the board need to be cut at?

If someone has a 2'' wide board and a 1 1/2'' wide board, and they want to cut the narrower board at an angle so the cut is 2'' long and the boards will fit together, what angle do they need to cut ...
-2
votes
2answers
38 views

If a 16' ladder is placed correctly on a level surface, how high up will the ladder reach?

So i have just began learning about sin cos and tan, and i came across this problem and for some reason I'm having trouble figuring it out. *** When using a straight ladder, it is recommended that ...
3
votes
1answer
35 views

Explain why two right triangles, each with an acute angle of 17 degrees, must be similar.

Two right angles with an acute angle of 17 degrees must be similar because triangles that are similar share the same angles.Is this proper?
16
votes
4answers
1k views

The position of a ladder leaning against a wall and touching a box under it

I was reading a newspaper and there was a little math riddle, I thought "how funny, that's gonna be easy, let's do it" and here am I... The problem goes as follow : in a barn, there is a 1 meter ...
0
votes
1answer
30 views

Find angles between sides of triangle and coordinate planes ($xy,yz,zx$ planes) using three 3d vectors .

Given the following, three vectors: \begin{align*} \vec{a}& = 3i−2j+5k, \\ \vec{b}& =i−6j+6k, \\ \vec{c}& =2i+3j−k, \\ \end{align*} find the angles between sides of triangle and ...
1
vote
3answers
46 views

Is it possible to find the vertices of an equilateral triangle given its center point?

I was wondering how to find the vertices of an equilateral triangle given its center point? Such as: ...
0
votes
2answers
52 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 ...
1
vote
2answers
62 views

Minimum value of cosA+cosB+cosC in a triangle ABC

I have used jensen's inequality but couldn't move on.
0
votes
2answers
38 views

How would you find the length of a side of a triangle where 2 sides are known and the length of a line in the middle is also known?

How would you find the length of a side of a triangle where the other 2 side lengths are known and the length of a another line that meets at the same point is known? I know there has to be an answer ...
0
votes
1answer
54 views

Proving that $ ABC$ is similar to $DQP$

Let $G$ be the centroid of triangle $ABC$. Let $D$ be the midpoint of $BC$. A line through $G$ parallel to $BC$ meet $AB$ at $M$ and $AC$ at $N$. $MC$ meets $BG$ at $P$ and $NB$ meets $CG$ at $Q$. ...
2
votes
0answers
44 views

Alternative proof for the equality of two angles in an isosceles triangle.

From the answers of my previous question, I got an idea to prove equality of two angles in an isosceles triangle. In that question the equality of two angles in a right-angled-isosceles triangle was ...
1
vote
1answer
51 views

How to prove AKN is an equilateral triangle? [closed]

Let $ABC$ be an equilateral triangle. $P$ is the midpoint of arc $AC$ of its circumcircle, and $M$ is another point on the same arc. $N$ is the midpoint of $BM$. $K$ is the foot of the perpendicular ...
2
votes
0answers
29 views

Generalization to higher dimensions of a statement about plane triangles

Let $\Delta=\Delta ABC$ be a plane triangle with area $F_\Delta$ and let $P$ be a point in $\Delta$. Draw lines through $P$ parallel to the sides of $\Delta$; then $\Delta$ is decomposed into three ...
3
votes
3answers
82 views

How is $\sin 45^\circ=\frac{1}{\sqrt 2}$?

I've been reading about the proof of $\sin 45^\circ=\dfrac{1}{\sqrt 2}$ in my book. They did it as following, let $\triangle ABC$ be an isosceles triangle as shown, Since the triangle is isosceles ...
-2
votes
2answers
41 views

Elementary problem in geometry [closed]

The problem asks to find the angle at $C$. The distance between $A$ and $B$ is $12 \space m$ and the distance between $B$ and $C$ is $8\space m$. Anyone got an idea?
-2
votes
1answer
24 views

Question related to triangles.

I am stuck at a question: O is a point in the interior of ∆PQR , then which of the following is true: 1)$(OP+OQ+OR)<1/2(PQ+QR+PR)$ 2)$(OP+OQ+OR)=1/2(PQ+QR+PR)$ 3)$(OP+OQ+OR)>1/2(PQ+QR+PR)$ ...
0
votes
2answers
41 views

Special triangles

I have this question that I have the answer to but no working how to get it, is it by pure memorization of angles or there some steps? Without a calculator, determine, in radians, the angles of a ...
2
votes
4answers
32 views

Prove that the co-ordinates of the centroid of a triangle is an average of that of vertices

For a given triangle [ABC], how do I prove that the co-ordinates of the Centroid $O_{xy}$ (intersection of the medians) is the average of the individual vertices? $O_x = \left(\frac {A_x + B_x + ...
2
votes
3answers
47 views

Find out the angles in a given triangle

In a $\Delta ABC$, $a=7$, $c=9$ & $\angle A=36^\circ$. The values of $\angle B$ & $\angle C$ are a.) $94.91^\circ$ & $49.09^\circ$ b.) $95.4^\circ$ & $48.6^\circ$ ...
-4
votes
0answers
38 views

Why do the triangles in the unit circle after 90 degrees look like this?

e.g. any triangle in the unit circle has one side (the hypotenuse) which is always positive? why is it positive? I edited this picture http://mathforum.org/mathimages/imgUpload/Trig_refangle.jpg to ...
2
votes
0answers
18 views

Maximal Triangle on Sphere [closed]

If en equilateral triangle is drawn on the surface of a sphere and expanded till its three vertexes coincide in one point, how many sections result?
0
votes
1answer
33 views

Summation of Infinite Areas of Triangles Involving Median

A triangle has an area of 2. The lengths of its medians equal the lengths of the sides of a second triangle. The lengths of the medians of the second triangle equal the lengths of the sides of a third ...
2
votes
1answer
31 views

Maximal Triangle Partitioning in n lines

Recently I was given the following problem at work: Given a 5 pointed star, draw two straight lines through it so that there are 10 minimal triangles within the drawing. It took some work but I ...
0
votes
4answers
57 views

How to prove using Plane Geometry that Centroid divides in ratio $2$:$1$ [closed]

In $\Delta ABC$ Can any one give me a hint to Prove that the centroid $G$ divides $A$ and Mid point of $BC$ in the ratio $2$:$1$ Using only Plane Geometry.
4
votes
1answer
117 views

Module of the differential of a function

Given two triangles, $PQR$ and $P'Q'R'$ in $\mathbb{R}^2$, I want to find a bijection $f$ between $PQR$ and $P'Q'R'$ such that: 1) $f$ maps vertices in vertices and sides in sides (i.e. $P$ in $P'$, ...
0
votes
2answers
51 views

A triangle has sides $2n, n^2+1$ and $n^2-1$ prove that it is right angled

I've tried using Pythagoras theorem but it always results in a silly answer like $n=n^2$ or something. I'm nearly 100% sure this is done with Pythagoras but I'm not sure which way to do it
1
vote
1answer
35 views

Parallelogram inside of a triangle dependencies

APMH is a parallelogram inside the triangle ABC. It has a perimeter of 18cm. So my question is could MP divide AB by 2 equal parts AP and PB???
0
votes
2answers
60 views

Prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third and half as long

The task is to prove that the line segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long. (Or in vector notation PQ = AB / 2). It should be proved ...
0
votes
0answers
23 views

Given verticies find the area of the triangle formed

When I looked at this problem I didn't think it seemed all that hard until I actually tried it. The problem is this: Given the rectangular vertices $O(0, 0, 0), P(-1, 2, -3), Q(-2, 3, -4), R(0, 0, ...
-1
votes
0answers
28 views

The minimum perimeter and maximum height of a triangle under constraints [unanswered] [duplicate]

I need a second oppinion: Please, i need urgent help for my very difficult question, many days ago i ask this question, now , i only have 7 days for present my http://triancal.esy.esTriancal (online ...
0
votes
1answer
22 views

How to work out the angle of a line passing through a plane

I have a triangular plane composed of three points. From this it it easy to deduce that the plane is in fact composed of two vectors which must touch at some point. because all of this is relative, ...
1
vote
2answers
60 views

Calculus made easy Exercise 9 Question 4 (Doubt)

A piece of string 30 inches long has its two ends joined together and is stretched by 3 pegs so as to form a triangle. What is the largest triangular area that can be enclosed by the string? I took P ...
3
votes
2answers
51 views

Expected value of area of triangle

Here is the problem: Let $A$ be the point with coordinates $(1, 0)$ in $\mathbb R ^2$. Another point $B$ is chosen randomly over the unit circle. What is then the expected value of the area of the ...
1
vote
2answers
46 views

Trigonometry in triangle, can't understand an example from my textbook

I'm stuck with this from a few hours. There is an exercise in my textbook, which is solved and it's must be used as an example, however I can't understand it. Here's the exercises + how it's solved. ...
2
votes
1answer
18 views

Reference request- Darboux cubic of a triangle

Hi everyone on Math Stackexchange, I'm recently interested in the geometry of a triangle, and my studies now seems to require some knowledge on cubic curves related to a triangle, in particular the ...
0
votes
0answers
21 views

Inequality based on triangle sides [duplicate]

Let $a,b,c$ be the sides of a triangle. Prove \begin{equation}(a+b-c)(a-b+c)(b+c-a)\le abc\end{equation} I assumed that $a\le b\le c $. Then $(a+b-c)\le a$ and $(a-b+c)\le c$ but $(b+c-a)\ge b$
1
vote
1answer
60 views

Homework Geometry Triangle Proof Help? (high school)

The question is: Prove that connecting the feet of the altitudes of a given triangle, we obtain another triangle for with the altitudes of the given triangle are angle bisectors. I've tried using ...
0
votes
0answers
18 views

Find A or B only given the hypotenuse and A to B ratio of a right triangle?

I'm looking for a formula (or set of formulas) that would be able to determine the A, or B value given a right triangle when only C and the A:B ratio is known. I want this mostly for personal use with ...
0
votes
0answers
27 views

Energy of a Triangle Wave

I want to find the energy of two triangular functions (identical, one above ( S1(t) ) and the other below ( S2(t) ) the x axis, so it should be the same thing). They are shown in the images below. The ...
2
votes
2answers
104 views

What do you call the point where two lines meet?

This is from a third grader. His example is the point where the hands on the clock meet. It's not pivot. Or "if you start with a dot and make two lines go out from it, on straight up and one to the ...
2
votes
3answers
58 views

Given point in triangle, prove that it is the centroid

So the question goes like this: Given a triangle ABC, there is a point M within that triangle such that [AMB]=[AMC]=[BMC]. Prove that M is the centroid of the triangle. ([AMC] denotes the area of ...
2
votes
2answers
22 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
34 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?
1
vote
0answers
68 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 ...
4
votes
2answers
52 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
37 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
50 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 ...