# Tagged Questions

3answers
13 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?
0answers
15 views

### Find next point in ellipse given the chord length

I would like to draw a cloud programmatically. For this reason I need to know where to draw the next circle around the ellipse. Given the chord (circle radius), how can I calculate the next point in ...
1answer
32 views

### Find the value of $\tan^2\alpha+\cot^2\beta$

A circle with centre o have two chords AC and BD,which are intersecting each other at P.If $\angle AOB=15^\circ$ and $\angle APB=30^\circ$,then find out value of $$\tan^2\angle APB+\cot^2\angle COD$$ ...
1answer
47 views

### Drawing an arc between two points

I was writing a java program to draw an arc. Arc2D.Double(int x,int y,int width,int height,int startAngle,int arcAngle,int type); Since, I'm not familiar with the mathematics behind drawing arc, I'm ...
1answer
61 views

### How to find a point on the tangent line whos length is 1?

im trying to figure out a formula to find the point(x,y) on a tangent line whos length is between 0 and 1 while it rotates around the unit circle uniformly, so the point would either be right on the ...
3answers
60 views

### Distance between two antennas

I am trying to find out the formula to calculate how high antennas need to be for Line of Sight (LoS) propagation. I found: d = 3.57sqrt(h) also ...
2answers
43 views

### Calculate new positon of rectangle corners based on angle.

I am trying to make a re-sizable touch view with rotation in android. I re-size rectangle successfully. You can find code here It has 4 corners. You can re-size that rectangle by dragging one of ...
3answers
40 views

### Please help me find a formula to find the 3rd point in a right triangle

I'm trying to figure out how to plot a 3rd point on a graph Given the following line segments and angles Is there a formula for the 3rd point? Note: This image is just for an example. The base ...
1answer
27 views

### Please help me to find an equation to find the 3rd point in an arc.

Long story short, I want to animate the rotation of an object that's based off a circle. Given the center point of the circle, the radius, and one of the points in the arc, is it possible to find the ...
0answers
20 views

### How can I align the angle between points with the magnetic heading as the points move?

I have 3 robots which must track a point. The distance between all the robots and the point is known so a triangle can be formed between any 2 robots and the point. If I find the angles in the ...
1answer
38 views

### Optimal rotation to align a circle with external points

I have a circle $C$ with radius $r$ and a set of finite points $P=\left \{ p_1,p_2,\ldots,p_n \right \}$ are identified external to the circle $C$. These points may lie on the exterior or the interior ...
1answer
60 views

### finding Length of a diagonal

Given Quadrilateral ABCD in such that $AB<BC<CD$ creating increasing arithmetic progression with sum of $27$ cm. $\measuredangle BCD=60^{0}$. the diagonal $BD=\sqrt{133}$ cm, and it divided ...
2answers
116 views

### Calculating circle radius from two points and arc length

For a simulation I want to convert between different kind of set point profiles with one being set points based on steering angles and one being based on circle radius. I have 2 way points the ...
1answer
18 views

### What is Angle(A,b) about something.

I was reading a paper and came through a notation saying .... Angle = Angle(A,B) about C. Can anybody tell me what exactly it means. Thnaks, Harsha
1answer
21 views

### Need “up” vector to calculate distance from a focal plane given world coordinates (SOLVED)

I have a RGB image, and for each pixel in the image I also have its real world coordinate. I also have the location (real world coordinate) yaw, pitch and roll of the camera. I am trying to produce ...
0answers
43 views

### How to find the maximum diagonal length inside a dodecahedron

I am trying to find the maximum length of a diagonal inside a dodecahedron with a side length of 2.319914107*10^89 meters. I am not sure if any other information than that is needed, if it is I ...
1answer
56 views

### Euclidean triangle. Does this one exist

Does $\exists$ a Euclidean triangle $ABC$ with $\sin(A) : \sin(B) : \sin(C) = \frac{1}{4} : \frac{1}{3} : \frac{1}{2}$?
1answer
26 views

### Largest Quadrilateral from a Set of Points

I posted the below on StackOverflow but was directed here as this may be more mathematical problem but I was looking to implement an algorithm.... I have a discrete set of points. From this set of ...
0answers
12 views

### Is there a formula to get the changes in ship course from wind and current?

Anyone know how to get the changes of degree's in ship course that affected by wind and current? I thinks it maybe related with the speed and degree of WIND and CURRENT. But I don't know how to ...
1answer
62 views

### How can I calculate the angle of a slice of an ellipse?

I'm attempting to draw a pie-chart programmatically, using an ellipse instead of a circle, but I'm having trouble calculating the correct angles for the slices. If it were a circle, I could use the ...
1answer
17 views

### Coordinates of all 'N' points, equidistant from each other , on a circle of radius 'R' whose center is (h,v) from the origin?

How would I calculate the coordinates of all 'n points' equidistant from each other on a circle of radius r and the center coordinates of (h,v) from the origin .
1answer
40 views

### How to find a new point on rectangle based on an known point on the same?

I have rotated a rectangle a certain amount of degree and got the point(x,y)=(130,40) which was previously (152,60). Now i want to find the x,y(marked as red) value at another location based on the ...
0answers
34 views

### Geometry question

The sides of a triangle are given to be $x^2+x+1$ , $2x+1$ and $x^2-1$. Then the largest of the three angles of the triangle is a)75 degree b)$\dfrac{x}{x+\pi}$ c)120 degree d)135 degree please ...
1answer
98 views

### How to simplify this trigonometric expression?

I was trying to solve a problem taken from an Physics Olympiad when I came across a curious and complex mathematical expression. I can not prove with what I know so far about mathematics, does could ...
1answer
59 views

### Calculating mean velocity of an orbiting body as it moves towards a point.

I'm making a game, in the game planets orbit a central point in circular orbits, they move directly towards their targets and the vector is simply added to their orbital path. Whilst not realistic it ...
1answer
34 views

### Trig problem, finding angles and ranges

I have what may well be a simple problem, but it's been too long since I've done this type of problem. From a fixed point (intersection of all the lines), the angles to 3 other fixed points $a,b,c$ ...
2answers
49 views

### How do I find the surface area of an angled conic base?

Thank you for viewing my question. I need help creating a formula for finding the surface area of a conic base. (eg. I install a flood light on my roof, I want to know how much surface area it will ...
3answers
113 views

### How can I find the points of intersection between the curves $r=1+\sin\theta$ and $r=1-\sin\theta$?

Find the points of intersection for the curve $r=a(1+\sin\theta)$ and $r=a(1-\sin\theta)$ My book says the answer is $(0,0),(a,0),(a,\pi)$. However I calculated $(a,0),(a,\pi),(a,2\pi)$.
3answers
58 views

### Proofs on equilateral triangles

Let $\Delta$ be the set of all triangles with two equal edges and be inscribed in a circle of radius $R$. So, how do I show that: Equilateral triangle in $\Delta$ is maximizing the area? and this ...
2answers
131 views

### Hard proof concerning the periodicity of trigonometrical functions. Is that a challenge or just trivial

i want to know if exist or if you can develop or give me ideas of a proof to show that the least number for which sine is periodic is $2\pi$ \neg \{\exists n\in \mathbb{R} \wedge n < 2\pi: ...
1answer
87 views

### Is this a valid proof of the derivatives of the trigonometric functions?

For the sake of this proof, the trigonometric functions $\cos$ and $\sin$ are defined as the coordinates of a point on the unit circle, rather than any of the modern analytic definitions. Let \$\vec ...
2answers
89 views

### Can find the angles of the triangle created by 3 points if I have each points compass bearing?

I am currently researching using magnetometers and radio field strength of 3 points for localisation. Is it possible to use the compass heading of 3 points to work out the angles of the triangle they ...
3answers
104 views

### How to prove $\cos\left(\pi\over7\right)-\cos\left({2\pi}\over7\right)+\cos\left({3\pi}\over7\right)=\cos\left({\pi}\over3 \right)$

Is there an easy way to prove the identity? \cos \left ( \frac{\pi}{7} \right ) - \cos \left ( \frac{2\pi}{7} \right ) + \cos \left ( \frac{3\pi}{7} \right ) = \cos \left (\frac{\pi}{3} \right ...
0answers
19 views

### Distance from a point outside of a sphere to two related points on the sphere, also angles needed

I'm a chemist with a solid background in maths, but I would really appreciate some help with the following problem: I have a point $M$ and a sphere. I only know the distance from the point $M$ to the ...
1answer
58 views

### $\tan B\cdot \frac{BM}{MA}+\tan C\cdot \frac{CN}{NA}=\tan A.$

Let $\triangle ABC$ be a triangle and $H$ be the orthocenter of the triangle. If $M\in AB$ and $N \in AC$ such that $M,N,H$ are collinear prove that : \tan B\cdot \frac{BM}{MA}+\tan C\cdot ...
2answers
71 views

### $\sin{\frac{A+B}{2}}+\sin{\frac{B+C}{2}}+\sin{\frac{C+A}{2}} > \sin{A}+\sin{B}+\sin{C}.$

Help me please to prove that: for any $\triangle ABC$ we have the following inequality: $$\sin{\frac{A+B}{2}}+\sin{\frac{B+C}{2}}+\sin{\frac{C+A}{2}} > \sin{A}+\sin{B}+\sin{C}.$$ It's about ...
1answer
25 views

### The law of cosines for a sphere

$\cos(c) = \cos(a)\cos(b) + \sin(a)\sin(b)\cos(C)$ Prove that if $a$, $b$, and $c$ is approximately $0$, then $c^2 = a^2 + b^2 - 2ab~\cos(C)$. I wasn't sure how to prove this. One thought I had was ...
5answers
151 views

### elegant proof that $\sin(x)\cdot\cos(x)=\sin(2x)/2$

I tried for a few days to prove the identity $\sin(x)\cos(x)=\frac{\sin(2x)}{2}$ and finally got the following proof. I wanted to know if someone knew a simpler or more elegant way to proof it. ...
2answers
42 views

### Area of a rectangular triangle

We need to calculate the area of the triangle shown in figure: The text of the problem also says that: $\sin \alpha =2 \sin \beta$. What is the area of ​​the triangle?
0answers
114 views

### Finding side and angle of isosceles triangle inside two circles

I'm having a problem that I'm not sure how to solve (or if it's even possible). It's not homework, just something i'm struggling with for a project. :) Basically, there are two circles, represented ...
1answer
72 views

### A controlled trapezoid transformation with perspective projecton

I'm trying to implement a controlled trapezoid transformation in Adobe Flash's ActionScript using the built-in perspective projection facility. To give you an idea of how the effect looks like: ...
1answer
59 views

### Area of a Quadrilateral proof

Prove that the area of a quadrilateral is one half the product of the lengths of its diagonals and the sine of the angle between the diagonals.
2answers
48 views

### Duplicate quadratic Bézier curve with new start point?

I have Bézier curve as shown by the wikipedia gif here: I would like to create a new curve that is a segment of the old one. For example, in this gif (from the same article): .. if I wanted B to ...
2answers
152 views

### The distance from a point to a line segment

I'm pretty sure this may be a duplicate post somewhere, but I've searched all through the internet looking for a definite formula to calculate the distance between a point and a line segment. There ...
1answer
47 views

### Finding the coordinates of a point five units along the line perpendicular to a midpoint?

I've been doing some personal math stuff and have spent the last few hours trying to figure this out with no success. I want to find the coordinates of the point at the end of the small line segment ...
1answer
134 views

### Trigonometry / Geometry Puzzle with a Circle Inscribed within a Square

Point P is any point on the inscribed circle. You must prove that (tan(a))^2 + (tan(B))^2 = 8 I first moved point P down to the point where the square would be tangent to the curve to make the ...
1answer
32 views

### Given a unit circle, is there a diameter that intersect it in one single point?

This is false but this is what I have come up with: The circle can be written as $x=\cos\phi$, $y=\sin\phi$, $\phi \in \left [ 0,2\pi \right ]$ Denote now $t=\tan{\frac{\phi}{2}}$ and it follows ...
2answers
78 views

### radian measure problem help.

Find, in radians, the angle between the tangents to a a circle at two points whose distance apart, measured on the circumference of the circle is 350 ft., the radius of the circle being 800 ft. so ...
1answer
41 views

### Determine theta/radius line parameters from line segment endpoints

I've been working on this for the past few hours and am quite stuck! As part of a computer vision exercise I've build a Hough transform that maps between the (x,y) space of an image, and a parameter ...
1answer
99 views

### Trigonometry and Geometry

I have no idea on how to solve this question so can someone please assist me. My son brought it from school and he is really struggling with the question. Consider a triangle ABC with line segments ...
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