# Tagged Questions

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### Calculation for the chance of finding something a given distance from a starting point by walking straight in a random direction?

The premise is basically a 2D plane with a single point, the starting point. Now a landmark sought by a hiker is a certain distance from that point. If the hiker can only see 1 mile in any ...
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### Different Definitions Of The Sine Function

I was hoping someone could give me a flow chart or high-level map connecting all of the definitions of the sine function, with some of the reasons why we care next to each. I've tried this but I'm not ...
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### The bird pointer problem: finding the angle of rotation

Suppose we have a bird pointer. He is a guy that likes to point at birds in the sky: His legs cannot move, however he can rotate around his torso. Also, his body and his arm always make a right ...
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### Conversion of angle from 360 degree to-90 degree

Here i am trying to convert angle into +90 degree AND -90 DEGREE FORMAT.For desired elevation angle i got answer properly.How to converert angle -90deg to zero, zero to +90 degree format. you can ...
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### Trigonometry-how to do? [on hold]

AB (3m) is an advertisement board perched on pole BC. CD is a horizontal ground level. AD=12m and BD=10m. Find the length of elevation of A from D and B from D. Find the length of BC.
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### Thinking of sohcahtoa with 90 in a triangle.

I know the answers from a unit circle. But when looking at a triangle how do you interpret Angle C sin C = cos C = tan C = I know the cos 90 = 0 and ...
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### Why is $\sin(d\Phi) = d\Phi$ where $d\Phi$ is very small?

I haven't touched Physics and Math (especially continuous Math) for a long time, so please bear with me. In essence, I'm going over a few Physics lectures, one which tries to calculate the Force ...
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### Solving right triangle given the area and one angle

Given right angle triangle $ACB$ (C is the right angle) has an area of 224 $mm^2$, what is the length of leg b if angle A equals 31.7deg? Here's the scenario: I have one right triangle completely ...
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### Similar triangle, Quick question (Thick Lens Formula)

http://www.panohelp.com/thinlensformula.html On the right hand side, f is defined as focus of the lens, i understand why the image distance is (f + fm). However i have spent an afternoon and could ...
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### Finding a 3rd coordinate of the rectangle points in 3d

I have a 4 3-D-points, each of them has only 2 of 3 known coordinates, as follow (? is unknown here): P5 (P5x, P5y?, P5z) P6 (P6x, P6y?, P6z) P3 (P3x, P3y, P3z?) P4 (P4x, P4y, P4z?) They build ...
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### A cycloid that goes through the beginning and through a general point

Parametric equations of the general cycloid through the beginning $(0,0)$ are $$x(t)=\frac{2t-\sin2t}{2d}$$ $$y(t)=\frac{1-\cos 2t}{2d}$$ How can we determine $d$ such that the cycloid goes through ...
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### Find the relation the 'maps' 2D points to the corresponding 3D images.

I have this [on hold] question (#857264) re-phrased. Hope that the content is more meaningful now. The following is the picture modified from the original. The question is a rectangular piece of ...
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### Why does this get the angle of the surface?

I have this (physics) question, but am missing something as to why the math works for it. The problem is as follows: A 4- kg sphere rests on t he smooth parabolic surface. Determine the normal ...
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### How to normalize a slope?

Say I have two slopes and two averages for a sample: $m=4{,}000$ dollars/day, average $a=50{,}000$ $n=80{,}000$ dollars/day, average $b=700{,}000$ Graphically, $n$ is very ‘steep’ compared to $m$. ...
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### If $(A_1A_2)^2 + (A_1A_3)^2… + (A_1A_n)^2= 14r^2$, then prove that the number of sides is 7.

Let $A_1, A_2,\ldots,A_n$ be the vertices of a regular $n$ sided polygon inscribed in a circle of radius r. If $(A_1A_2)^2 + (A_1A_3)^2+\ldots + (A_1A_n)^2= 14r^2$, then prove that the number of ...
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### what does secant equal 2 mean? [duplicate]

I need your help, I am a little confused. My question is, what does the value of secant mean? I asked this question previously but unfortunately I did not understand the answers so I am trying to ...
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### Vector Magnitude during rotation

Probably something I should now already but this is confusing me no end! Lets say we have a force which is directed at 69 degrees inclination (from the X axis) with a magnitude of 500, shown below: ...
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### Circle area and lim

I was trying to show how to find $\pi$ value from formula $\pi R^2$, but I dont understand where is my mistake. So i am calculating area using $n$ triangles 1 let $R=1$, then one triangle area is ...
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### Finding an area of a triangle inside of a triangle, given certain areas of other triangles, and area ratios.

I'm studying for the Waterloo Math Contest (Galois, Gr. 10) taking place in April of 2015 and I am preparing by looking at previous problems and solving them. This is question 4(c) on the 2010 Galois ...
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### Points for which $AX^2-BX^2$ is constant

My problem is from Israel Gelfand's Trigonometry textbook. Page 9. Exercise 8: Two points, A and B, are given in the plane. Describe the set of points for which $AX^2-BX^2$ is constant. I would ...
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### Elementary Trigonometry problem

My problem is from Israel Gelfand's Trigonometry textbook. Page 9. Exercise 7: Two points, $A$ and $B$, are given in the plane. Describe the set of points $X$ such that $AX^2+BX^2=AB^2.$ The ...
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### Get the angle in a circle using center, radius and one point in a circle.

There is a circle and i know Point1 this is fixed and i know another point Point2 which can be anywhere in the circle. and i want to know the angle which is made at center. Thanks Your help will be ...
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### Find points near end point of a line

Any equation to find points near to both start and end points of lines with different slopes. See image. Need P and Q. If Endpoints are named A and B, AP and BQ should be 1 cm
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### Proving Sin Cos Tan

I am asked to prove the following: $$\dfrac{1-\cos x}{\sin x}=\dfrac{\sin x}{1+\cos x}=\tan\dfrac x2.$$ Looking at the answer I am not able to see what is going on here: \frac{1 - ...
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### Bounding box of a thick line with end caps

I have been pulling my hair out on the trigonometry on this and just can't seem to get it right. Basically, I need to calculate the bounding box of a line going from point (x1,y1) to (x2,y2) where ...
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### Find length of $CD$ where $\angle BCA=120^\circ$ and $CD$ is the bisector of $\angle BCA$ meeting $AB$ at $D$

$ABC$ is a triangle with $BC=a,CA=b$ and $\angle BCA=120^\circ$. $CD$ is the bisector of $\angle BCA$ meeting $AB$ at $D$. Then the length of $CD$ is ____ ? A)$\frac{a+b}{4}$ B)$\frac{ab}{a+b}$ ...
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### Get a third point (lat, lng) from two given

I have two points as follow (the distance between them is variable): I need to get a third as shown: The two first points change all the time, including the distance between them. My problem: I ...
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### Find the circle touching a line

I have been struggling with this (probably easy to solve) geometry problem for a while. What are the coordinates of the centre and the radius of the circle?
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### Alternatives to polar coordinates for mapping point onto one dimensional coordinate

I can map a point (x,y) to polar coordinates (angle,length). However, let's say in this (angle, length) pair, "length" doesn't actually interest me, so I can map (x,y) to a one dimensional ...
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### Hyberbolic and Circular (Trig) Functions: Why no parabolic? [duplicate]

There are circular (trig) functions which determine all the points on a unit circle: and which relate to the area swept out by an angle subtended on the circle. -- These functions can of course be ...
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### Weird inequality answer, truncate or round?

When arriving at the final answer for a double inequality question, it appears that my text book has truncated one part and rounded the other. Is there some weird inequality rule that I don't know ...
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### Issue with the geometric proof of lim_{x -> 0} sinx/x = 1

When proving $\displaystyle\lim_{\theta \to 0} \frac{\sin\theta}{\theta} =1$, I have been taught to use a sector with radius 1. How rigorous is this proof if we have not considered a radius of any ...
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### find the height of the tower

A person standing at a point $A$ finds the angle of elevation of a nearby tower to be $60^{\circ}$. From A, the person walks a distance of $100 ft$ to a point $B$ and then walks again to another point ...
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### What is the theorem called that states that equal angles gives equal sides?

We have an isosceles triangle, what is the theorem called that states that the sides opposite it's congruent angles will have congruent lengths? Could someone also explain why this is.
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### What is the relationship between the area of a triangle and an area of a segment of a circle?

I had a very smart physics teacher in the past remind us of the area of a segment of circle through this 'derivation': "well, if you put two of those together doesn't it kind of look like a ...
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### Find probability of angle being obtuse

We are given points A and B on the 2D plane and distance between them is 2. Let C - randomly picked point on the circle with radius R and center at the middle of AB. Find probability of angle ABC ...
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### Inscribed circle: find distance to circumscribing circle

Let a circle with center $b$ and radius $r$ be contained in a circle with center $a$ and radius $R$. Given a point $c$ on the small circle, find its distance to the greater circle. That is find the ...
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### Is it possible to solve this series of triangles with only the given information?

Consider the following: As displayed in the picture, the distance between the points is 1, so the last point's coordinates would naturally be $(c, d+4)$ Is it possible to solve for the coordinates ...
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### Find Area of 3 Sector Circle, Variable center point

I have a Circle separated into 3 sectors. At start each sector has the same central angle, 120°. Therefore each sector should be taking up the same area. I want to be able to move the center point ...
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### smaller circle into larger circle : find length of common arc

Let a circle of radius $r$ be contained in a larger circle of radius $R$ such that the two circles touch. What is the length, in radians of the common arc, in blue? I think the solution is ...
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### Moments at which moving points on a circle coincide

Points A $(0,1)$ and B $(1,0)$ start moving along the circumference of a unit circle with center $(0,0)$ in the same, positive (that is, counterclockwise) direction. Every minute, points A and B ...
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### what triangles have rational ratio in side and angle? [duplicate]

It's the same with the title, what triangles have rational ratio in side and angle? I mean, what triangles have rational ratio among sides and angles?
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### Rationality in Triangle

How can I justify this answer? I think the answer is infinite, but cannot justify it///
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### Determining the angles of a triangle given the ratio between its edges

Given that a triangle has edges of ratio 2 : 3 : 4, the task is to determine the three angles, say in degrees. I started by drawing 4 cm segment on the paper, then drew perpendicular segments of ...
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### Equation of tangent on Cartesian plane given center and radius of a circle

If I have a generic circle with radius $r$ and center $(h, k)$, and a tangent line with point of tangency $(x, y)$, can you give me the equation of the tangent line? Thanks!
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### Angular velocity of the minute hand

The exercise is to calculate the angular velocity (in radians per hour) of the rotation of: the hour hand, and the minute hand (of the clock). Neither of my answers coincides with the answers in ...
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### How to determine the visibility of an object from the top of a hill

We are developing software to train children how to cross the street safely. Part of the training is to teach them not to cross when they don't have enough visibility due to obstacles. In this case, ...
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### Solving for an angle using trigonometry.

Trying again $\dfrac{\sin(180 - \theta - a)}{H + R} = \dfrac{\sin(a)}{R}$ $\dfrac{\sin(\theta + a)}{ H + R} = \dfrac{\sin (a) }{ R}$ (is this correct?) \${\sin(\theta + a)} = \dfrac{{ H + R}}{ ...