Trig problem, it shouldn't be tough, but it is

[devout parcel]

One degree is 111m of x

Basically, I got this function

Problem: when alpha tends to 90, the height tends to 0, and it can not tend to 0, as it is constant

Goal: Learn how can I improve the function to keep h constant, as it is in "reality"

[honest jasper]

What exactly needs to be found?

[devout parcel]

let's say a balloon, it's mostly a numerical problem, no statement, no context

Or is it needed

I think, that the 111m per degree is the causer

[honest jasper]

No, I mean I don't exactly understand what's going on in the problem.

[devout parcel]

I have to guess h By any method, simpler better

i only have alpha

Well

I don't have to guess the height

I have to create a function

height depending on the angle

Anything remaining to explain?

[honest jasper]

Well, are there any ther restrictions? Because what I can see doesn't restrict the height of h at all.
I can see that the lines AA and BB are parallel, that's no problem. But that doesn't restrict the length of BB.

[devout parcel]

well

alpha is from 0 to 90

[devout parcel]

BB has the same length as AA

We can call C and D the bottom ones

[honest jasper]

Oh, I see! Then it's easy.
tan(β) = AA/x
AA = x tan(β)
h = x tan(β)
In terms of α:
h = x cot(α)
You said that when α -> 0, we have h -> 0. That is only valid when x is constant.

[devout parcel]

In fact, X is alpha*111m

Each degree is 111m in the surface

[honest jasper]

What is 111 m?

[devout parcel]

meters

[honest jasper]

Wait, wait. Degrees can't be meters. Degrees measure angles, length measures lines.

[devout parcel]

I know

But there's a relationship

For each degree, the surface is 111m

Like the Earth's latitude

[honest jasper]

Not sure if I understand.

Which surface?

[devout parcel]

x

In this case

Do you get it? Or still no clue hehe

[honest jasper]

x can't depend linearly on α.

[devout parcel]

Is there any way to make it depend on α?

[honest jasper]

Well, x = h tan(α).

[devout parcel]

And, if x is linearly dependant on α, what errors should I expect?

[devout parcel]

Oh okay

[ornate ether]

so Tan(1°) = (x/111) / h