# What is Angles: Definition and 907 Discussions

The Angles (Old English: Ængle, Engle; Latin: Angli; German: Angeln) were one of the main Germanic peoples who settled in Great Britain in the post-Roman period. They founded several kingdoms of the Heptarchy in Anglo-Saxon England, and their name is the root of the name England ("land of Ængle"). According to Tacitus, writing before their move to Britain, Angles lived alongside Langobards and Semnones in historical regions of Schleswig and Holstein, which are today part of southern Denmark and northern Germany (Schleswig-Holstein).

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1. ### I Antipodal points and temperature and other angles

Hello, I am a high school math teacher and recently presented my students with an intriguing problem: "At any given moment, there are two antipodal points on Earth (180 degrees apart) that have the same temperature." This can be demonstrated using one great circle with two opposite points. If...
2. ### How to Calculate θ3 After Finding θ2 Using Snell's Law?

I used Snell's law to find θ2 as 40,1 (3sf) but now I'm stuck on finding θ3. Is there a way to find θ3 without using geometry? How do I do this?
3. ### Solve for all angles x: cos(2x) + cos(x) = 0, where 0<x<2pi

I'm not sure how to go about solving this mathematically? In just using what seems obvious, I know the angle pi would work, because pi = -1, and 2pi = 1. However, as far as manipulating the equations in a way where it can solve itself without me having to look at a chart where cos for both x...
4. ### B A Question Relating Sum of Angles and Breaking of the Parallel Postulate

Question: What is the relationship between the sum of the angles of a non-euclidean triangle being greater or less than 180 degrees and the definite breaking of the parallel postulate? Is the proof of this trivial? Edit: Additionally, can we say that if the angles of a triangle sum to greater...

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6. ### I Error in Euler angles and quaternions

Hi, I got a set of Euler angles and a set of quaternions, and I wanted to compare each set against its corresponding set obtained from STK, and I was wondering what would be a good indicator to measure the error between the Euler angles I got and those from stk , and the same for quaternions...
7. ### Finding the angle that a string makes with a wall and its tension

For a better understanding of this exercise here is the image illustrating the scenario described in the statement: So to solve this exercise I began by drawing a forces diagram: I believe I have explained everything in the "Relevant equations" section. What am I doing wrong? The book that...
8. ### Discover Circle Theorem Help for Triangle PST: PSR Angle = 77 Degrees

From triangle PST, angle PSR = 180-(81+22) =77 degrees sum of angles in triangle. Is my attempt correct?
9. ### Find the area of the quadrilateral OCBAO

My challenge was on trying to determine the angles: My approach; came up with a number of equations: ie ##m+n=70^0## ##r=p+40^0## ##q-2r=100^0, ⇒ r=50^0 + \dfrac{1}{2} q## then it follows that, ##2q+100^0=180^0## ##⇒q=40^0, r=70^0, p=m=30^0, n=40^0## ##m+40^0+t=180^0, ⇒t=110^0## and...
10. ### A Corresponding case of steady precession but for Tait-Bryan angles

(This has continued to bother me. I tried asking, and no response. May I please try again?) Using Euler angles, we rotate about an axis (often, axis three of a gyroscope frame), then a second (axis one of the gimbal frame), then return to the same axis as the first one (back to axis 3, but of...
11. ### Two roads meeting a river at different angles (heights and distances)

Problem statement : I copy and paste the problem as it appears in the text. I hope am understanding its wording correctly.Diagram : The river is shown in blue. The two roads start from the crossing C and end in A and B, making angles ##60^{\circ}## and ##30^{\circ}## resectively. The longer of...
12. ### A formula involving the sum of cosines of the angles of a triangle

Problem Statement : The statement appeared on a website where a different problem was being solved. I got stuck at the (first) statement in the solution that I posted above 👆. Here I copy and paste that statement from the website, which I cannot show : Attempt : To save time typing, I write...
13. ### Sum of angles with x,y and z axis made by a vector

I want to know if there is any proper relation between the angles of a vector with the three dimensional coordinate axes, if the angles are ,α , β and γ, will the sum of α, β and γ be 180 degress that is α + β + γ = 180°,m finding the same to be true in a 2 D case where α + β = 90° and γ =...
14. ### Interpolate between 2 impact points only given the throw angles

Top-Down-Perspective: At first I am quite sure that the problem is not solvable since there are that many unknowns. But my Approach would be to create a linear function with P1 and P2 and then set it equal to the function that gets me the impact location of P3 and then solve it by b3. Thanks...

Question: Where is an angle of 10.5π radians in standard position located? A. On the positive vertical axis B. On the negative vertical axis C. In the second quadrant D. In the fourth quadrant I thought I had to divide 10.50 by 3.14, which I thought yielded 3.34π. Then I subtracted 3.34π...
16. ### I How can Euler angles be visualized using a polar plot?

Dear Forum, say I am projecting an ellipsoid along the z-axis to the xy-Plane. The resulting ellipsis is rotated around the z-axis by the angle gamma until the principal axes coincide with the x- and y axis. Now before projecting, I rotate the ellipsoid first around the z- and then around the...
17. ### Understanding the Differences between Euler Versus Tait Angles

Good Morning! I understand that the definitions and notations used for Tait–Bryan angles are similar to those described above for proper Euler angles, and I can work problems in either. However, I lack the ability to "rise above both" and categorize them. I do understand that the only...
18. ### A Why are Euler's angles picked exactly that way?

So the Euler's angles are described like this: xyz-x'y'z' (first rotation around z axis) x'y'z'-x''y''z'' (second rotation around x') x''y''z''-XYZ (third rotation around z'') So I've been thought it goes like this, now I'm wondering why? Why exactly these angles and why this order? Why can't it...
19. ### Find angles such that the motion travels a specific distance

We know the time it takes the water complete the whole parabola is (sin(x) * 6.5 * 2) / 9.8. So I come up with (sin(x) * 6.5 * 2) / 9.8 * cos(x) * 6.5 = 2.5, because the x component of the velocity is the same for the whole time. But I get the results like these: x≈0.30929171+πn,1.26150461+πn...
20. ### Relative Velocity and Angles of Movement (Sears & Zemansky's Exercise)

The official solution says ±25.4°, but I'm having trouble reproducing it. Here is my solution: 1) The components of the velocity of firework F with respect to the ground G in the moment of explosion are the following (Notice, I'm using sin, because the statement says 30.0° from vertical.)...
21. ### I Triangles on Spheres: Isosceles and Shortest Distance Inferences

If I have a triangle on a sphere with two of its angles 90 degrees each, do I conclude that it's isosceles and that the shortest distance (on the sphere) beteeen the base and the vertix of the thid angle is 1/4 the circumference of a great circle on the sphere? This is the picture I have in...
22. ### I What's the definition of angle in a curved space embedded in a higher Eucledian space?

I don't want to post this in a math forum because it's very basic and I just want a straightforward answer, not something math heavy . What's the definition of angle in a cuved space embedded in a higher eucledian space? Like when I have a spherical surface in 3d eucledian space and want to work...
23. ### Load and Stress; 3 angles with different shapes corners

Summary: Each angle has a different type of corner, rectangular, circular, and triangular. Which one is the strongest? All three angles are mounted in the ground and made of the same material. The same force ‘w’ towards the ground is acting on all angles, which one is the strongest? Please...
24. ### MHB Difference of angles in a triangle

In a triangle ABC, let D and E be the intersections of the bisectors of the angles ABC and ACB with the sides AC and AB, respectively. Knowing that the measures in degrees of the angles BDE and CED are equal to 24 and 18, respectively, calculate the difference in degrees between the measures of...
25. ### Conceptual question involving tension and angles

I have actually already partly solved a), as I do get the concept behind how to find tension through making sure that the net force in the x and y direction are zero. Here are my answers for a) T1 = T5 = 2mg/sin(theta) T2 = T4 = mg/sin(phi) T3 = mg*cot(phi) The reason I am asking this...
26. ### I What are the significant angles between intersecting planes in 4D space?

Suppose I have two intersecting planes in a four dimensional space. It seems to me that there are two angles between these planes. If the two planes intersect in a line then one of those angles is zero. If the two angles are non-zero then the planes intersect in a point. If one plane is the...
27. ### I Interesting angles between 10~~25º ?

NOT a home-work / college question, merely wondering... Just as there are 'interesting' numbers, per primes, Pythag' triples, Euler-stuff etc, are there any 'interesting' angles between 10~~25º ?? I've had a hunt around, noticed several possibilities invoking eg transcendental fractions of...
28. ### B Calculating the Angle Between Virtual Sources of Fresnel's Biprism

Why is the angle in radians when we calculate the distance between the virtual sources of Fresnel's biprism??
29. ### Calculate distance from a point 100m from a plane given two angles

I am looking for a formula. From a horizontal plane of 100 meters; If angle on the left is 8 degrees and the angle on the right is 21 degrees at what distance from the centre of the horizontal plane will these two angles converge?
30. ### Simultaneous Trigonometric Equations - solving for angles

Summary:: I have a series of three equations that transform three angles of a system (J1, J2, J3), into three spatial x, y, z coordinates. I want to invert them to find the angles from the coordinates. Reference: https://www.physicsforums.com/forums/general-math.73/post-thread I have a series...
31. ### Proving three angles are equal if they satisfy two conditions

Problem Statement : I copy and paste the statement of the problem directly from the text. Attempt : I wasn't able to go far into the solution. Below is a rough attempt. ##\begin{equation*} \begin{split} \sin^2A-\sin A\sin B+\sin^2B-\sin B\sin C+\sin^2C-\sin C\sin A & = 0\\ \sin A(\sin A -...

33. ### Find the contraction of angles seen by an observer

I am trying to follow the work to this question but am stumped at steps 3 and 4. I am confused as to where the cos^2(90+θ) comes from? I can see it is used to invoke sin into the equation since we have that value. Is it because we are only measuring the x-component of the movement, so we need...
34. ### Solving Physics Problem with Angles and Trigonometry

The correct solution uses angles and trigonometry. My solution is as following: - Suppose the forces exerted by friends 1 and 2 are F1 and F2 respectively. - There are no net force in the x-direction, so F(total x) = 0. - F(total y) = F1 + F2 - mg = 0 (initially). Rearranging gives g =...
35. ### Multiple angles : Reducing the sum

Problem Statement : Let me copy and paste the problem as it appears in the text : Attempt : I haven't been able to make any significant attempt at solving this problem, am afraid. I tried to reduce all the higher submultiple angles ##2\theta, 4\theta, 8\theta## into ##\theta##, but the...
36. ### Trigonometric ratios of angles above 90 degrees

I have been doing the resolutions of vectors on x and y-axis with making triangles and reference angles in all quadrants. But I want to calculate now how to find something like ##\sin 235## without the help of reference angles. I know we don’t need to. Calculator and Taylor theorem is handy here...
37. ### Finding Multiple Angles from Sine Values on the Unit Circle

I got 41 and correspondingly 49 from this. It said its wrong

39. ### I Math Myth: The sum of all angles in a triangle is 180°

From @fresh_42's Insight https://www.physicsforums.com/insights/10-math-things-we-all-learnt-wrong-at-school/ Please discuss! We all live on a globe, a giant ball. The angles of a triangle on this ball add up to a number greater than ##180°##. And the amount by which the sum extends...
40. ### Complementary Angles: A Visual Explanation

I thought I understood it until I found the statement mentioned. It's obvious having a look at Figura 3.53: ##\cos \alpha=\dfrac{OP_1}{OP}\Rightarrow{OP_1=\cos \alpha}##, ##\sin \alpha=\dfrac{OP_2}{OP}\Rightarrow{OP_2=OP\cos \left({\dfrac{\pi}{2}-\alpha}\right)=OP\sin \alpha}##

42. ### MHB Trig Angles: Equations & Solutions

I need only equations on this one
43. ### MHB Draw Angles & Find Values in Unit Circle

Hey! :giggle: Make a drawing for each of the values of the angle below indicating the angle at the unit circle (in other words: $\text{exp} (i \phi )$) and its sine, show cosine, tangent and cotangent. Give these four values explicitly in every case (you are allowed to use elementary...
44. ### Finding angles with Bragg's Law

Part (a) Ok so for (a) ##\theta_{incident} = \theta_{reflected}##, so I assume I could just consider the horizontal planes in these atoms. ##n\lambda = 2a\sin(\theta)## ##p = \frac {h} {\lambda}## ##\frac {nh} {2amv} = \sin(\theta)## ## v = \frac {nh} {2am\sin(\theta)}## I suppose the...
45. ### Cosine of Angles 120, 60, 30 - Math Solution

120, 60,30 cos 120 = -0.5, cos 60 = 0.5, cos 30 = 0.866
46. E

50. ### MHB Computation of bond angles and other angles in tetrahedral

Hello, I didn't understand the geometry of molecules in which central atom has no lone pairs of electrons. for example, in $CH_4, NH_4^+$ molecular shape is tetrahedral and bond angle is $109.5^\circ$. How is that bond angle computed? $CH_4$ stands for liquid methane and $NH_4^+$ is a...