Trigonometry Problems

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 90°. 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 90° 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

Pretty basic stuff but I guess I don’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.

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

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?

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

The question:

Prove that:

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

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

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?

I am currently reading for Dummies series of those math books and they are quite good as introduction and I really like them. But I have feeling that there can be much more extensive coverage of topics, more details and much more ways of doing same things. Can you please suggest book(s) that cover all (or nearly all) sides in great details for for Algebra I, Algebra II, Geometry and Trigonometry?

And each problem has 3-5 parts

Pretext: As with many things I was figuring numbers and rules for D&D, and in this particular instance I am looking at the Warlord Fighter subclass for 5e. And it states that you may designate an area with a side no longer than 10ft. Similar text can be found in very, very few cases without an upper bound like "within a 5ft cube" as an example. One such other case is Minor Conjuration from the Conjuration Wizard, which is 3ft of any side/length instead of 10ft.

The problem: So although it would likely be ruled at a game table that this becomes a 2×2 square (1 square is 5ft long) the base game does not actually call for a grid to be used. And this is where I got the concept: if this were not bound to a grid, how large could the designated area be? For simplicity sake I chose the smallest integer of 1 degree external angle, making a 360-gon. Now I personally neither have the tools to draw out a repeatable process nor the knowledge of possible shortcuts. But what I want to figure is the distance between the segment A and it's parallel on the opposite side. In this case, all 360 segments are 10ft and naturally at 179d internal angles.

The expression: One could certainly continuously repeat the process to eventually 'build a ladder' on a graph with the next 178 segments, but I was more curious if someone new of a shortcut expression to find the answer.

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 θ

1.) sin θ=1/2 ,cos θ= √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 θ.

1.) tan θ= 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 20° + cos^2 20°

2.) sec^2 28° − tan^2 28°

3.) sin 80° csc 80°

4.) tan 50° − (sin 50°)/(cos 50°)

5.) cot 25° ⋅  csc 65° ⋅  sin 25°

6.) sec 35° csc 55° − tan 35° cot 55°

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

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

a. cos 60°

b. cos^2 30°

c. csc π /6

d. sec π /3

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

a. sec^2 θ

b. cot θ

c. cot( π/2 - θ)

d. csc^2 θ

My son recently participated in the 2019 AMC 8 Mathematics Competition. Now that the competition is over, I am helping him understand how to solve some of the problems he did not get. I have been able to show him how to solve all of them except for Problem 24. The answer key says that 30 is the correct answer.

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.

I need help with my Trig Homework since I’m not getting some concepts. Anyone willing to explain and guide me through the 8 or 9 problems for an hour or less would be greatly appreciated!

While standing at the left corner of the schoolyard in front of her school, Suzie estimate that the front face is 8.9m wide and 4.7m high. From her position, Suzie is 12.0m from the base of the right exterior wall. She determins that the left and right exterior walls appear to be 39° apart. From her position, what is the angle of elevation, to the nearest degree, to the top of the left exterior wall?

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 = √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 :)

My solution so far: https://imgur.com/a/tNp17eK

Question: In triangle ABC, A = 30°, AB + AC = 19 cm, and the triangles area = 19,5 cm2. How long is AB.

I've written everything I know but can't find the solution and any help would be appreciated.

Hello can someone help me with my very hard trigonometric problem, I don't know how to solve it.

Solve in R the equation : sin(x- π/6).cos(2x+ π/3) = sin(2x+ π/3).cos(x- π/6)

Thanks

"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 :)

https://www.analyzemath.com/Trigonometry_problems/trigonometry_problems.html

Question 4 is what gets me.

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.

How does he go from the above equations to h = (1/Tan 20 - 1/Tan 60) ?

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?

I know how to do A, but I got B and C wrong. The way I did it for B was change my calculator to radians, and plug in cos(2.333) (2.333 being the radians). I got -0.690734037 but the correct answer was -0.62168232577. For C I plugged in sin(2.333) and got 0.723108907 but the correct answer was 0.65077729356.

If anyone knows how to get the correct answers I'd appreciate it ! Thank you.

https://imgur.com/a/AySkDUP

I’m not sure how to approach this problem. I don’t understand it. Could someone please help if possible? My class has not done a problem like this before. The photo under the problem is the diagram in color and clearer. If anyone could help that would be amazing, thank you!

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!

https://i.ibb.co/zNDfDgT/20190722-230836.jpg

It seems like a simple algebra problem but despite trying different methods I can't seem to get the correct answer. I'm not sure how to get to the last step from the second last step. Can someone help me out?

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 ∈ ℝ.

a,b ∈ ℝ

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

I’ve been doing the Khan Academy Trigonometry course and I am on the part about the law of cosines and the law of sines. I’m not sure how to attach a picture as this subreddit doesn’t allow pictures so I’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 can’t work out how get that as neither the law of cosines or the law of sines seem to apply.

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

Can anyone help me understand this?

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