# Tagged Questions

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### 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.
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### Length of a line in an isosceles triangle. (mind boggling )

In an isosceles triangle ABC, side AB and AC are equal in length. There exists a point D on the side AB. The angle BAC is theeta . The side AD is two units smaller than AC .What is the generalized ...
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### A triangle has to find its third side.

Problem: (Euclid had a triangle in mind - I am including this line so that future googles come across this question) The triangles longest side is $20$ and another side is $10$. Its area is $80$. ...
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### Crazy rectangles, semi-circles, and circles!

Problem is to find the ratio of the area of the circle to that of the semi-circle. Note that points $F$ and $E$ weren't given in the original diagram, and that the circle at the top-right ...
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### Proving congruency of triangles

Question: Given $AB$ is diameter, $C$ and $D$ lie on circumference, $AB = 15cm$, $AC = 12cm$, $BD = 9cm$, find area of quadrilateral ABCD. Note that the points $O$ and $Q$ were not in the ...
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### Equilateral triangle inscribed in a ellipse

"Given any point on a ellipse, is it always possible to inscribe an equilateral triangle, with a vertex coincident with that point, in the ellipse?" I thought I could use analytical geometry, but ...
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### Distance to the point of intersection of two altitudes in a triangle

Problem $P,Q,R$ are the points $(4,2)$, $(2,1)$ and $(6,-3)$. Also, $PS$ and $QT$ are altitudes in this triangle. A) Find the equations of PS and QT My answer: PS: $y-x-2=0$, QT: $5y-2x-1=0$ ...
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### Computing Euler Angles from Direction Cosines Vector

My problem simply as the following: Suppose we measured the orientation of a plane object with respect to a reference fame. (where the reference frame parallel to plane frame). The unit normal vector ...
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Prove that $\|a\| + \|b\| + \|c\| + \|a+b+c\| \geq \|a+b\| + \|b+c\| + \|c +a\|$ in the plane. Gentle hints only, please! I know that attempting to decompose R.H.S. into $$\alpha a + \beta b + ... 1answer 43 views ### 3x+3y-1,4x^2+y-5,4x+2y are sides of an equilateral triangle I am completely lost in this one 3x+3y-1,4x^2+y-5,4x+2y are sides of an equilateral triangle, its area is closest to the which integer? 0answers 63 views ### Probability of a triangle in a circle [duplicate] I'm confused on my calculations on analytic geometry with probability. Things I learned on these were messed up since I was a newbie on these subjects. Here's my problem: Three points are chosen ... 1answer 113 views ### Triangle problem (only know 1 side and y-axis coordinates of 2 points) I have a triangle problem that I am in desperate need of help with with. Here is what I know ... the triangle is mapped on a graph where I only know y-axis coordinates for 2 points, the length of one ... 1answer 349 views ### find the rate of change of the area of triangle pulled by three people from its sides this is the problem of my curious mind(I am it's designer!) . three people each having the rope attached by the end of the 3 sides of triangle ABC , pull the triangle with speed U in the direction ... 1answer 117 views ### Triangle optimization problem Let a,b,c be the sides of a triangle , then what is the maximum and minimum values (if exist) of the following quantities (i) \dfrac {a^2b^2c^2}{(a+2b)(a+2c)(b+2c)(b+2a)(c+2a)(c+2b)} (ii) ... 2answers 192 views ### Geometry - Area of Siamese Triangles How can I find the Area of this figure? It is quite curious because it is a particular case of this sequence: Anyone know how to find the area of this sequence as a function of the number of ... 2answers 590 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 = ... 1answer 178 views ### Algebra question about Triangle Interiors I was reading about Triangle Interiors on Wolfram Alpha: http://mathworld.wolfram.com/TriangleInterior.html and they have a simple equation:$$\mathbf{v} = \mathbf{v}_0 + a\mathbf{v}_1 + ...
Given: $A = (0,0)$ $B = (0,-10)$ $AB = AC$ Using the angle between $AB$ and $AC$, how are the coordinates at C calculated?