hyperbolic function catenary problem

An electric cable strung between supporting posts, takes the form of the following curve, which is called a
catenary, and which has the following relationship:
𝑦 = a cosh (𝑑/2a)

a = minimum height above the ground of the cable
d = distance between the supporting posts
(i) If the height of the posts is 10 m and the minimum height of the cable above the ground is
8 m, determine the distance between the posts.
(ii) Determine the length of the cable s, between the posts in (i) above, given by the following
equation:
𝑠 = 2a sinh ( 𝑑/2a)

the formula y = a cosh (d/2a) will only have a single value for y.... is there something missing ?

https://media.cheggcdn.com/study/5f3/5f3b4ac0-588f-449e-854b-c27215a6b1c9/image
y would be the height of the support posts a distance d apart, so its not really a curve ... Though it sort of is if you regard d as a variable and not related to the support posts ...

Thanks for this. I've been overthinking it

Are you ok with it now? It should just be a couple of lines.

Thanks for this. I've been overthinking it

the formula y = a cosh (d/2a) will only have a single value for y.... is there something missing ?

Are you ok with it now? It should just be a couple of lines.

Hello, I'm struggling with the working for this. I keep coming up with d=2a(y/acosh) but am unsure if this is correct. Any help is hugely appreciated.

Think I need to do some more reading on this as I'm a bit lost by that... Guessing my rearrangement is a bit off?

Its wrong. As per the previous email cosh() is a function and you need to use the inverse function arcosh() rather than dividing by cosh. If it was cos() instead of cosh() could you do it?

I'm quite rusty but do you mean to use cosh^-1 to cancel out the original cosh and work it from there?

Yes, assuming cosh^(-1)() is the inverse function and not the reciprocal 1/cosh()

An electric cable strung between supporting posts, takes the form of the following curve, which is called a
catenary, and which has the following relationship:
𝑦 = a cosh (𝑑/2a)
a = minimum height above the ground of the cable
d = distance between the supporting posts
(i) If the height of the posts is 10 m and the minimum height of the cable above the ground is
8 m, determine the distance between the posts.
(ii) Determine the length of the cable s, between the posts in (i) above, given by the following
equation:
𝑠 = 2a sinh ( 𝑑/2a)

Am i way off here, or, they are not looking for exact numbers, ie d =11. rather the 2 equations you would use to determine the numbers. to me, without either the distance between posts or the length of the cable, you cannot resolve to an exact value?

Its better to start your own thread, but youre told values for y and a and have to do a relatively simple rearrangement of the first equation to get the value of d for part i).