Vector math/trigonometry/relative positions problem

I've been trying to solve this on my own, but I've reached a point where the more info I absorb, the more confused and aimless my attempts become.

I'll explain what I'm trying to do with the attached image.

PANEL 1:

This is the basic setup. Three points (represented by sprites within a Node2D, the only nodes involved here), (a) and (b) are dynamic (more on this later), (c) is fixed and cannot move at all.

PANEL 2:

The points are positioned (and should ultimately move) in such a way that if I were to draw a triangle/two triangles as shown, the highlighted angle would always be exactly 90Β°. On top of this, the three sides of the highlighted triangle should also have a fixed *total* length.

PANEL 3:

With this in mind, (b) should move towards the midpoint between (a) and (c) as (a) moves further away (and vice versa), so as to preserve both the 90Β° angle and the total sum of all side lengths.

I feel like there must be a simple method to do exactly this, I'm just finding myself having immense problems successfully applying any of the info I'm reading (including Godot's intro to vector math). It's like I can't see the forest for the trees, which is why I'm asking here.

Additional info:

My original plan was to calculate the midpoint between (a) and (c), then position (b) there with an offset along the y axis, get the distances between (a)-midpoint and (b)-midpoint, and finally reduce (b)-midpoint/offset as (a)-midpoint increases. This didn't work as intended, though.

I'd also like to mention that even though I talk about movement and positioning in my problem description, I don't need help with those aspects. I know how to move things around, I specifically need help figuring out the math that'll return the coordinates I need.

Thanks in advance.

https://preview.redd.it/4b1nlu9nwm651.png?width=1448&format=png&auto=webp&s=58b60ac6d51aa2c045974848ff3a23732ee8630e

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Pretty basic stuff but I guess I donβt understand the question really.

If A and B are acute angles, and A is less than B, explain why sinA is less than sinB.

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[Grade 10 mathematics, trigonometry] Here is the problem:

The airplane will take off at an elevation angle of 42 Β° at a speed of 320 km / h. What height does he climb to in 10 seconds?

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Trigonometry problem

Hello I am trying to find the length of two sides of a triangle with the help of another triangle but I seem to be getting something wrong.

I have a isosceles triangle and a right angled triangle (e means angle)

https://preview.redd.it/7z1u8hehb4x41.png?width=379&format=png&auto=webp&s=5492ab327e0d001a452eb08217f0d01bdd2e87e0

I know the values of e2, d, e1 and f

I reason then that e2 = e3 beacuse you can continue the line f and add two parallel lines at e3 and e4 using the transversal.

Then from there I can do: sin(e3)*f = fx

and (fx^2 + f^2)^(1/2) = fy

For some reason this is wrong, could I get some help understanding how to solve this?

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Grade 11 Math. [Trigonometry problem]

Trigonometry question

For the following information about a triangle, decide if the triangle exists. a=4.7cm, b=4cm, B=60 degrees. Justify your reasoning.

Im stuck in this question I do not know how to solve it

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The question:

Prove that:

tan ΞΈ/(1 - cot ΞΈ) + cot ΞΈ/(1 - tan ΞΈ) = 1 + tan ΞΈ + cot ΞΈ

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https://preview.redd.it/2oeyk2656nd41.png?width=1920&format=png&auto=webp&s=531607a9fb6b96a3dd46a096eb9e0b7776afa680

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https://preview.redd.it/co6sk7y6i0f41.png?width=935&format=png&auto=webp&s=cbfd37d91135914527e0c6ae029ce28f9e0b472e

So the sin(B)=b/c, I'm not sure how that helps me solve the problem other than setting up the Pythagorean theorem to solve for the variable. Is there a simpler way of working this one out?

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And each problem has 3-5 parts

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Hey everyone, I'm taking trigonometry right now as a college student. I've always sucked at trigonometry, even in highschool and it's finally coming back to haunt me. Anyways, homework isn't required in this class, but I'm trying to do some of it anyways and I don't even know where to begin when solving some of these problems. I wish the professor would have taken a problem from each of the sections in the homework and solved it as an example, So I could see how to do the steps exactly. I've taken 1 (or more) problem(s) from each section, I was hoping you guys could better explain this to me.

Section 1 : Use, Identities to find the exact value of each of the four remaining trigonometric functions of the acute angle ΞΈ

1.) sinΒ ΞΈ=1/2 ,cosΒ ΞΈ= β3 /2

Section 2: Use the definition or identities to find the exact value of each of the remaining five trigonometric functions of the acute angle ΞΈ.

1.) tanΒ ΞΈ= 1/2

Section 3: Use Fundamental Identities and/or the Complementary Angle Theorem to find the exact value of each expression. Do not use a calculator. (I included a few more on this section because there are a few different types.)

1.) sin^2 20Β° + cos^2 20Β°

2.) sec^2 28Β° β tan^2 28Β°

3.) sin 80Β° csc 80Β°

4.) tanΒ 50Β° β (sinΒ 50Β°)/(cosΒ 50Β°)

5.) cotΒ 25Β° βΒ  cscΒ 65Β° βΒ  sinΒ 25Β°

6.) secΒ 35Β°Β cscΒ 55Β° β tanΒ 35Β°Β cotΒ 55Β°

Section 4: Given (something) use trigonometric identities to find the exact value of...

1.) Given sinΒ 30Β° =1/2 use trigonometric identities to find the exact value of

a. cos 60Β°

b. cos^2 30Β°

c. csc Ο /6

d. sec Ο /3

2.) Given tanΒ ΞΈ = 4 , use trigonometric identities to find the exact value of

a. sec^2 ΞΈ

b. cot ΞΈ

c. cot( Ο/2 - ΞΈ)

d. csc^2 ΞΈ

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2019 AMC 8 Problem 24

I can find the area of a bunch of the triangles, but not the requested one. I am sure I am missing something simple. Any help would be greatly appreciated.

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I came across this question in my a level textbook, I can't quite understand it. Only some parts.

The cost of building a lighthouse is proportional to the cube of its height, h.

The distance, d, that the top of the lighthouse can be seen from a point at sea level is modelled by:

d = β2Rh

Where R is the radius of the Earth and d, R and h are in the same units.

Three possible designs X, Y and Z are considered in which the top of the lighthouse can be seen at 20km, 40km and 60km respectively.

Find the ratios of the costs of designs X, Y and Z.

Thank you in advance to the person who can explain it :)

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[Trigonometry] Vector word problem.

"You are traveling due West on Mineral at 30 MPH. A car traveling at an angle of 120 hits you on the driver's side of your car. A police officer stops you and the other driver. You claim the other driver was speeding and driving recklessly when he hit you. By doing some investigating on where your car landed, at 135, can you prove the other car was speeding? Otherwise you may have a hefty fine on your hands (The speed limit on Mineral is 40mph)". The angles are relative to standard position so that means the right triangles are going to be 30 60 90 and 45 45 I've tried to incorporate this into the problem using the theorems but I keep getting a point where (-30,0) (-a, av3) (-a, a) and that doesn't make sense. I feel like I need to know my cars final velocity at 135 but I probably just don't get vectors yet. Any help on how to approach this problem would be great :)

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I understand that Tan 20 = h/(10+x) and that Tan 60 = h/(x) but I don't understand the next logical jump made in the solution.

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Hello, I currently have a word problem I'm trying to solve.

Taylor is skiing on a circular ski trail that has a radius of 0.9 km. Taylor starts at the 3-o'clock position and travels 2.1 km in the counter-clockwise direction.

A. How many radians does Taylor sweep out?

B. When Taylor stops skiing, how many km is Taylor to the right of the center of the ski trail?

C. When Taylor stops skiing, how many km is Taylor above of the center of the ski trail?

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https://imgur.com/a/AySkDUP

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The problem in question:

https://imgur.com/a/DNHa68K

For this particular triangle, (3+3+6.4)/2 gives me an S value of 6.2. This means that when I plug in the S value as well as the side length values into Heron's Formula, I'm going to end up with a negative root, leaving me unable to solve the problem. I feel like something is off with my math here. Can anyone take a quick look at this and steer me in the right direction? Any help would be greatly appreciated. Thanks!

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[High School Trigonometry] - I'm stuck on a certain problem

Determine what a and b are such that the following equation:

a(cosx - 1) + b^2 = cos(ax + b^2 ) - 1

is correct for every x β β.

a,b β β

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Am i the only one who thinks that this problem on my trigonometry homework looks like a meme?
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Trigonometry Problem

Hey Reddit,

It has been too long since I have done trigonometry and as such I have lost the ability to know how to go about solving problems. I am looking to solve the below problem for X. If you need anymore information let me know but I am pretty sure that should sum up everything.

Also if possible could I find out what X would be without the height of the triangle being 15 and the shared angle of both triangles being 15 degrees?

Appreciate any assistance!

https://preview.redd.it/oapyueu7fih21.png?width=1320&format=png&auto=webp&s=fe8eebf2af4fff834cbb013aeb09fd522c21aedb

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How do I work out this trigonometry problem?

Iβve been doing the Khan Academy Trigonometry course and I am on the part about the law of cosines and the law of sines. Iβm not sure how to attach a picture as this subreddit doesnβt allow pictures so Iβll just describe the problem:

In triangle ABC, side AC = 89, side CB = 48, and angle A = 30 degrees. I need to find angle C, but I canβt work out how get that as neither the law of cosines or the law of sines seem to apply.

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Trigonometry Problem

I've tried solving it and get it from their solutions, but I still don't get it. Any ideas?

https://preview.redd.it/m1szc5wm7uy41.png?width=1034&format=png&auto=webp&s=a323987ca86dfb59d9861046ee30e65141b41ce8

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Maths Problem - Trigonometry

Can anyone help me understand this?

https://preview.redd.it/u1rbndiak0j41.png?width=1166&format=png&auto=webp&s=48235a06815fbb891eaca8504836796b6532a434

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