For questions about properties and applications of triangles

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4
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3answers
643 views

Pythagorean theorem expressed without roots in an old Tamilian (Indian) statement

There's an old Tamil statement that predicts the hypotenuse of a right angle triangle to a reasonable level of accuracy considering it doesn't involve roots. This is how it goes: “Odum Neelam ...
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1answer
25 views

How many different hands of 5 cards chosen from 52 are possible if the hands must have exactly 4 kings?

How many different hands of 5 cards chosen from 52 are possible if the hands must have exactly 4 kings? I know $_{52}C_5$ could come in somewhere here, but I'm not really sure how to get this. ...
3
votes
2answers
42 views

Find the Vertices of a Triangle from Set of Points

I have a set of cartesian x,y points which I know am fairly certain are on the edges of a triangle. What is the easiest way (either algebraically or algorithmically) to identify what the three ...
4
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2answers
83 views

Show that in any triangle, we have $\frac{a\sin A+b\sin B+c\sin C}{a\cos A+b\cos B+c\cos C}=R\left(\frac{a^2+b^2+c^2}{abc}\right),$

Show that in any triangle, we have $$\frac{a\sin A+b\sin B+c\sin C}{a\cos A+b\cos B+c\cos C}=R\left(\frac{a^2+b^2+c^2}{abc}\right),$$ where $R$ is the circumradius of the triangle. Here is my work: ...
2
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2answers
118 views

$\frac{AB}{A'B'}+\frac{BC}{B'C'}+\frac{CA}{C'A'} \geq 4 \left(\sin{\frac{A}{2}}+\sin{\frac{B}{2}}+\sin{\frac{C}{2}}\right). $

Let be a circle inscribed in the triangle $\triangle ABC$ wiht the center $I$. The intersection of the circle with $AI$ is $A'$, with $BI$ is $B'$ and with $CI$ is $C'$. Prove that: ...
0
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5answers
91 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 $59^\circ$, B is $55^\circ$, and C is $66^\circ$. (not to scale) thanks in advance
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2answers
42 views

How do I properly read a clinometer?

If the weight hangs down at roughly 42 degrees, would the angle be 90 degrees - 42 degrees = 48 degrees?
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3answers
33 views

What is the unknown angle?

So first off I started with the pythagorean theorem to find the missing leg of the triangle. \begin{align*} 5^2 + b^2 ={}& 8^2 \\ 25 + b^2 ={}& 64 \\ 64 - 25 ={}& 39 \\ \text{missing ...
1
vote
3answers
62 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
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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
2
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3answers
35 views

Triangle relationships

I was wondering if someone can help me actually. You see I came upon this book called Mathematics for Physics by Michael and Malcolm Woolfson. I a presently stuck on the very first exercise and I can ...
1
vote
2answers
865 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 ...
0
votes
5answers
160 views

Calculate the angles of a isosceles triangle

In the triangle below, is there a way to calculate the $x$ and $y$? To be more specific, $b = 12.8\rm\,cm\ $ and $h = 10\rm\,cm$, hence $a = 11.87\rm\,cm$. I don't know what to do from here.
0
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2answers
72 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 ...
2
votes
2answers
269 views

Triangle related question

My question is: In $\Delta ABC$, let $AE$ be the angle bisector of $\angle A$. If $\frac{1}{AE} = \frac{1}{AC} + \frac{1}{AB}$ then prove that $\angle A = 120^\circ$. What I tried: I extended side ...
0
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1answer
23 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 ...
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1answer
17 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
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1answer
2k views

Calculate new graph point with coordinate and angle

On a Cartesian graph I have a point at $x = 0$ and $y = 0$. This point needs to move forward at a $30^\circ$ angle. It should travel forward at this angle for $1.75$ on the graph. What equation can I ...
11
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3answers
2k views

How to prove $\Delta DEF$ is an equilateral triangle?

$\Delta ABC$ is an equilateral triangle and $AD = BE = CF$. Prove that $\Delta DEF$ is an equilateral triangle.
2
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1answer
395 views

Sum of Angles in a Triangle.

Can anyone please explain how to form a better idea in understanding sum of measures of angles in a triangle is $180^\circ$ ?
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2answers
378 views

How do i find this angle in a right triangle?

So I'm writing a program and I need to write a method that will give me the angle of a specific angle of a triangle when I know only the adjacent length and opposite length. I know that $\tan(A) = ...
0
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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 ...
0
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1answer
6k views

Determine angles of triangle given nothing (no scientific calculator) but triangle sides.

The question says it all. Given a triangle, find its angles without a calculator. Is this even possible without tables or making tables? Summary: Is it possible to determine the inverse sin, cos of ...
0
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2answers
38 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 ...
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2answers
41 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
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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?
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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 ...
2
votes
2answers
340 views

Barycentric coordinates of a triangle

I have to do what described in the picture below. Consider the planar triangle $[p_1,p_2,p_3]$ with vertices $p_1=\begin{pmatrix}-2\\-1\end{pmatrix}$, ...
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2answers
54 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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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: ...
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2answers
477 views

How to find the inradius of a triangle with given side lengths?

I need to find the inradius of a triangle with side lengths of $20$, $26$, and $24$. I know the semiperimeter is $35$, but how do I find the area without knowing the height? Thank you.
0
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1answer
304 views

A problem on triangle and its perpendicular bisectors.

I'm trying to solve the following problem : "In △ABC, coordinates of $B$ are $(−3, 3)$. Equation of the perpendicular bisector of side $AB$ is $2x + y − 7 = 0$. Equation of the perpendicular ...
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2answers
61 views

How to find the number of right angled triangles with integer sides and inradius 2009 ..

Problem : How to find the number of right angled triangles with integer sides and inradius 2009 Please help on this as I am not getting any clue how to proceed this problem. I know that ...
3
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1answer
349 views

Geometry - optimal 2D mesh between X expendable points

Say you have X points on a plane. If you connect two points, you form a line. Connecting three points forms a triangle. A line cannot cross a line, and a smaller triangle cannot be created inside a ...
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2answers
63 views
0
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1answer
512 views

Calculate 3rd point of a triangle, given 2 points and all angles in 2D

I have stumbled upon an interesting problem. I tried to find an answer here but there are just too many similar threads which did not really help me, so I was trying to figure it out by myself. The ...
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1answer
979 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 $C$.
0
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1answer
366 views

Can an equilateral triangle be an isosceles triangle, too?

I've looked in a math book that an isosceles triangle has at least two congruent sides. I also know that the words "at least" mean this symbol: $\ge$, which means "is greater than or equal to" or "is ...
4
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7answers
186 views

Proving $ \frac{1}{c} = \frac{1}{a} + \frac{1}{b}$ in a geometric context

Prove or disprove $$ \frac{1}{c} = \frac{1}{a} + \frac{1}{b}. $$ I have no idea where to start, but it must be a simple proof. Trivia. This fact was used for determination of resistance of two ...
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1answer
55 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 $Q$. ...
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2answers
39 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 ...
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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 ...
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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 ...
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0answers
31 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 ...
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2answers
7k views

How to find the third coordinate of a right triangle given 2 coordinates and lengths of each side

p2 |\ |b\ | \ A| \C | \ |c___a\ p1 B p3 If given point p1 & p2, side A & B how would you find point p3? I know given this information you ...
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2answers
1k views

Ratio of angle divided by a line drawn in triangle?

If a line drawn from one point of a triangle divides opposite side in ratio $1:2$ then in what ratio angle is divided by line?
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3answers
9k views

How to find triangle height?

I need to know the height ($h$) of a triangle with two unknown angles ($\alpha$ and $\beta$) and the known length of two sides $AB$ and $BC$. Is it possible to have that value of $h$ (height)?
3
votes
3answers
890 views

Right-angled isosceles triangles

If a right-angled triangle is isosceles then the other two angles must be equal to $45^\circ$ ? Is this always the case or are there other possible right-angled isosceles triangles?
3
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3answers
83 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 ...
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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?