# Tagged Questions

For questions about properties and applications of triangles

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### Problem finding coordinates in a earth like coordination system

A picture with the problem Hey guys Given: two coordinates $A(a_1,a_2), M(m_1,m_2)$ , the distance between $B$ & $C$ is known as $w, d(B,C) = w$ d(B,M) = d(M,C) where d is the great-circle ...
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### Determine vertex coordinates of a triangle if length and angles of opposite are known

Given a triangle such as this: Where $C$, $A$ and $B$ are cartesian coordinates and $a$, $b$, $c$ are the lengths of the sides. I know that $$C = (b\cos\theta,\;b\sin\theta)$$ where $\theta$ is the ...
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### Question to prove triangles Equilateral on provided conditions

Let D, E, F be points on the sides $BC,\ CA,\ AB\$respectively of a triangle $ABC$ such that $BD = CE = AF\ and \ ∠BDF = ∠CED = ∠AFE$. Prove that $ABC$ is equilateral.
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### Placing Pandas in a Triangle Pen

I am working on a bit of a silly problem in my introductory discrete mathematics course. I have five pandas that I need to place in a pen, and I have a pen that is the shape of an equilateral triangle ...
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### How would I solve for the bases of an isosceles without the height?

In the image below if you were to take 36 degrees and set it between 0-180 degrees how would you solve for the bases between points AC. There are special cases for the bases length such as (60 degrees ...
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### Area of Triangle in ellipse

Full question: Prove that the area of the triangle formed by three points of an ellipse, whose eccentric angles are $\theta , \phi$ and $\psi$ , is ...
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### Show that the perimeter of an octagon is $8(\sqrt{2} -1)$

My question is as follows: The top of a table is made in the shape of a regular octagon by cutting the congruent isosceles triangles from the corners of a $1$ m square piece of wood. Show that the ...
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### How can an angle be negative?

How can be angle be negative like sine(-60) , cosine(-50) ? Which quadrant do they fall if we have the negative angles ? I dont see any negative angles in full ...
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### Common meeting point for 3 points to reach 4th point [closed]

Problem statement: We are 3 friends at 3 different locations $A, B, C$ and want to reach a location $D$. Each person will take a separate cab to a common meeting point $E$, and then take a single cab ...
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### What does a triangle become?

I'll get to the point. Imagine a right triangle in 2D. If you move one of the points (not the 90 degree vertex) very far away, then the corresponding angle will become smaller as the point moves ...
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### In a triangle $ABC$,$AD,BE,CF$ are the altitudes and $R$ is the circumradius,then find the radius of the circle $DEF.$

In a triangle $ABC$,$AD,BE,CF$ are the altitudes and $R$ is the circumradius,then find the radius of the circle $DEF.$ This triangle is not given to be equilateral or anything else.Only the three ...
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### Help With Steps Of Finding Orthocenter

I'm trying to find the orthocenter of $M(-8,0)$, $N(0,0)$, $P(-4,6)$. I thought I did all of the steps right but I keep getting an answer of $(-4,6)$, but my book says $(-4,2.6667)$. Here are the ...
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### Line $x=-1$ is side BC of equilateral triangle ABC circumscribing circle $x^2 + y^2 = a^2$

An equilateral triangle ABC circumscribes the circle with equation $x^2 + y^2 = a^2$. The side BC of the triangle has equation $x = -a$. a) Find the equations of AB and AC. b) Find the equation of ...
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### How/why does this proportion work?

In this diagram, ΔXYZ is inscribed into the circles. O is the center of the larger circle. OZ=x, altitude XO=x-5, and OY=x-9. ∠XOZ and ∠XOY are both right angles. Using the two similar right triangles ...
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### Use a vector method to prove that the triangle is isoceles.

If two medians of a triangle are equal then prove by vector method that it is an isosceles $triangle$ This might be a simple question but i could not do it because i don't know any theorems related to ...
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### Find area of triangle which sides is limited by two functions and the x axis

I'm studying for my math exam and I'm stuck on the following question "A triangle is limited by the x axis and the two functions $y=kx$ och $y=\frac{1}{k}x+k$ where k > 1. Determine the smalest ...
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### Determine the height of the tree

Dylan is using his clinometer to help him determine the height of a tree. He stands 6 m from the base of the tree and takes the measurement shown on the clinometer. Then, he measures the height of ...
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### How to know what type of cross section is it going to be?

A plane intersects a right rectangular pyramid. Producing a cross section. The plane is parallel to the base. What shape is the cross section? I thought it would be triangle cause triangle cut is ...
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### The angles of the triangle given the position vectors of the triangle using the scalar product

I can't seem to show for question (a), I am not sure if it's because of my wrong calculation, or is it the question has the wrong values? What I have done is I used the scalar product. I found that ...
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### What is the approximate area of the shaded region of the given figure?

How do i find the area of the black shaded portion of the circle? I noticed the 4 so i think that's the radius. The formula to find the area $$A=πr^2$$ so I thought of using that to find the area ...
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### Finding the altitude of an isosceles triangle with base length and angle

So I have triangle ABC where: $AC = BC$; $AB$ is known $\hat C$ (the angle $A\hat CB$) is known I'm trying to find the altitude of said triangle.
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### Producing a 3D Net from a 3d inspired image

Producing a 3D Net from a 2D Image I'm trying to find the volume of the illustration, I've taken reference from the medium size of a strawberry's diameter, I've applied this scale to the remaining ...