Angle Definition and 1000 Threads

Ray $\overline{PK}$ bisects and the measure of $\angle{LPM}$ is $11x^o$ and the measure of $\angle{LPK}$ is $(4x+18)^o$ What is the measure of $\angle{KPM}$ $s.\ 12^o \quad b.\ 28\dfrac{2}{7}^o \quad c. \ 42^o \quad d. \ 61\dfrac{1}{5}^o \quad e. \ 66^o$

I'm making a program that generates lines in 3D space. One feature that I need is to have an incrementally increasing angle on a line (a bending line / curve). The problem is simple if the line exists in the xy-plane, then it would be a case of stepping say 1m, increase the azimuthal angle φ...

Hi all, a bit confused with regards to the whole term aspect angle. Most examples that I searched online involved either a 2D plane or a stationary object. In this case: Let's say the man is facing the ball. In this case, the ball is being thrown from the right to the left. Since the man is...

This problem just came to my mind when thinking on another problem. Does the tension is just 2T as it is if the angle "a" is 90 degrees? It seems not to me. In a "normal"( I don't really know what is the right word for that) situation, the tension is would be 2T at the line in the middle of two...

This is the problem I am working on at the moment. The question states that the bar is at rest in this state. At a 60 degree angle to the horizontal and supported by the vertical spring at B. Small oscillations are introduced and I am required to find the equation of motion and the natural...

Apologies if this is the wrong forum. I have an application where I need to measure the bend angle of a tube and display the resulting angle on a screen. I am using a laser mounted in a fixed location which reports distance back to my controller, (scaled to millimeters.) I am measuring from 92...

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Refractive index is a function of velocity in the medium. How is this related to deviation angle inside the medium? I am not asking for the known formula, but for the mechanism behind it.

Hello! I had a random question while playing around with a garbage can that I hoped y'all could help me walk through: Let's say that I have a hinge on a table, rotating with gravity acting perpendicular to it. Energy is provided into the hinge, let's say by a spring, like so: I want to know the...

Initially, I calculate the moment of inertia of of a square lamina (x-z plane). Thr this square is rotated an angle $\theta$ about a vertex and I need to calculate the new moment of inertia about that vertex. Can I split the rotated square to two squares in the x-z plane and y-z plane to find...

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I know you find the static friction of an incline by raising it until it begins to move and then measure the tangent of that angle, but I'm not sure how I'm supposed to show a relationship or create a procedure based off that.

My answer is (A) since I think the motion of the spacecraft will alter the length of the spacecraft (length contraction) but not changing the orientation so the angle will stay the same But my teacher said my answer is wrong. What is my mistake? Thanks

I am trying to find the launch angle ##\theta## using the relationship: ##\theta=\arctan(\frac{v_{y}}{v_{x}})## So, ignoring attenuation due to air resistance, we have a constant horizontal velocity: ##v_x = d_x/t = 95m/4.5s \approx 21 m/s## But what value do we use for ##v_y## which is not...

When a heavier mass (or nucleus say) collides with a lighter one, it deflects through a certain angle which has a theoretical maximum. There are numerous derivations for this maximum angle of deflection ##(\sin\theta_{d_{max}}=m/M)## where m is the small mass and M the larger but none seem to...

I would like to conduct an experiment asking the question "how does the angle at which a projectile is launched vary with respect to the horizontal range it covers?" Ultimately, I'd like to prove that the horizontal range is directly proportional to sin(2(theta)). This will be done with the aid...

I am trying to design an acrylic light pipe that has a 3W power red LED input with 60 degree beam angle. I need a reasonably collimated exit light beam or at least a narrow angle output. What I'd like to know is - what is the optimum shape of the exit end of the light pipe to produce the...

Einstein first calculated the bending of light rays that are touching the sun as 1.75 arc-sec. For the calculation I refer e.g. to https://www.mathpages.com/rr/s8-09/8-09.htm I know that spatial angles in general relativity don’t have an intrinsic value (are not invariant). They are dependent...

How does sound reflect from interface at an angle? The propagation of light is determined by a single factor - index of refraction. Sound is affected by two factors - speed and acoustic impedance. Take the case of two substances with identical acoustic impedance but different sound speeds - one...

I tried to find the components of the vectors. ##a_y =2.60 sin 63.0 = 2.32## and assuming the z axis would behave the same as an x-axis ##a_z =2.60 cos 63.0 = 1.18## ##b_z =1.30 sin 51.0 = 1.01## making the same assumption ##b_x =1.3 cos 51.0 = 0.82## I now think I should have switched these...

Hi! I really can't figure this one out... I have a = (F-cos(36.1)g) = a and from that I get T = mB1 a = 6.3 (20.3736) = 128 N. Could someone please help? Thanks!

In discussing flight mechanics with a (15 years younger) co-worker with a doctorate in Aerospace Engineering. We examined some angles and I happened to mention bisecting an angle. I told him in High School in the early 1970's we learned how to bisect an angle with compass, and straightedge...

Hello, I solved this problem two ways and got the same value for the magnitude but different values for the angle. I am wondering which is correct. I showed my work, so I hope someone can tell me if one method is just invalid.

Find the angle between the vectors v=-5\sqrt{3}i+5j and w=5i

Let $ABC$ be a triangle with $\angle A= 60^{\circ},$ and $AD,BE$ are bisectors of $A,B$ respectively where $D\in BC, E\in AC.$ Find the measure of $B$ if $AB+BD=AE+BE.$

Now i was just doing some random study and i saw this problem on the internet. The problem was to find angle ##B## now there were several responses, let me screen shot one that i think was a bit straightforward... my question is, "is there a much simpler way to find the angle ##B##"?

There are actually several questions. The formula for calculating the "beam angle" of light (emitted from lights bulbs, flashlights etc) is - α = 2 arcCos ( 1 - Lm ÷ ( 2 π Cd )) Where, α = beam angle in degrees Lm = luminous flux (Lumens) Cd = luminous intensity (Candela) The above formula...

Hello, Regarding the wave oblique angle propagation and based on Balanis "Advanced engineering Electromagnetic" book on page 136 ( it has been attached) I need to know why the phase velocity in x direction is not important to keep in step with a constant phase plane( Just equation 4-23). I...

The actual problem can be found as #2 on this link: https://ocw.mit.edu/courses/mechanical-engineering/2-71-optics-spring-2009/assignments/MIT2_71S09_ups1.pdf I rewrote the problem above with the solar irradiance data that they give. My interpretation is of a square 1 m x 1 m plane sitting...

I imagined the bar slipping along a virtual displacement, with the top and the bottom slipping by equal amounts. Since the planes are orthogonal, I took the components of these displacements: the lower end is displaced Lsinα in the direction of the right plane and by Lcosα in the direction of...

Attached is the picture of the belt. The angle of wrap seems to be >180 degrees.

distance (metres) Angle of elevation (degree) 950 7 1500 12 1800 15 3300 20 I think I don't need to use information about 900 metres because the path starts from elevation of 1000 metres. I imagine the distance will be the hypotenuse of a triangle and the height of a certain location...

Hi, I want calculate the m = slope of a linear line WHEN I already know the angle in degrees of the line. Here is an example: I calculate with Excel the angle with the following function: =+DEGREES(ATAN(0.0874887)) and I get as result the angle of 5%. But how do I calculate the value...

Hi, solid elements used in FEA don't have rotational DOFs so normally it's not possible to read the angle of twist from simulation involving torsion. Some programs allow the transformation of results to cylindrical coordinate system but it's not always the case. From what I've heard, it's...

Literally, don't know how to start.

I'm given an ultra-high energy cosmic ray with energy 10^20 eV. It is coming from a source 10 Mpc away with an extragalactic magnetic field with strength B = 10^-9 G. I am to determine the maximum angular deflection of this cosmic ray, so it hits Earth. I don't have an attempt of the solution...

Good Morning All. I have asked this before, but my post was not clear (my fault: I apologize). I hope this is more clear (please be patient as I try to get to the core of my confusion). In the first figure, below, the spinning top precesses as shown (well, it is not a animated jpg, but it...

If I assume the nebula is a circle, than the length of arc viewed from Earth is a half of the circumference. So, here $$l = \frac{1}{2} \pi D$$ From the problem, ##D = 125 000 ly##. Because the distance of nebula is much larger than the diameter; I try to approximate R with the distance of...

OK wanted to see how a transparent image would look like here:unsure: well first $\angle{BAC}=57^o$ by alternate interior angle are equal and then...

Hey guys, I'm struggling trying to figure this out and need some assistance. Not sure if I'm in the right category or needing the angle or what. But the goal is to prove Ex.1 is much smaller of an angle than Ex.2 and to be able to use the formula on a universal scale. Ex1: A=190, B=222, C=195...

the angle of incidence at A is 40°, then why did the answer key say "angle of incidence at A is just less than 90°". it is obvious that 40° is quite far from 90° right?

Please see attached drawing which I have written my work (in colour). Despite spending 1h on it I still can’t understand how to find angle BAC.

The destructive interference equation for small angles is angle=wavelength/(2a), where a is the width. I assume it means destructive interference since its talking about areas where no light is present. Using the equation after changing degrees into radians I get the answer of 2491 nm when the...

I think it has to do with conversation of momentum and projectile motion.

Two forces each of size 8N, have a resultant of 13N. a) Find the angle between the forces b) The two given forces of magnitude 8N act on a particle of mass m kg, which remains at rest on a horizontal surface with no friction. The normal contact force between the surface and the particle has...

In a process of writing a game. Effectively need to know how to angle the barrel for the projectile to hit the selected target. So for the equation y = h + x * tan(α) - g * x² / 2 * V₀² * cos²(α) Everything except α is known. Could anyone more wise in the ways of science than me help me solve...

If we know the change of angle is twice the incident angle, then the rate of rotation is 2*100 rpm = 200 rpm. Is there a better explanation of it?

So far all I know is that n1 and n2 represent the refractive indices of the two media, and so is theta (I think). Please help