Hard Trigonometry Problem help

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Hi. I have this pesky little trigonometry problem for homework (see link for photo). Normally, I would be able to solve it but there is no adjacent side given. The problem asks to find 'h'.

The only reasonable attempt I have made is making a proportion. I did:

58*/58ft = 46*/h

When I solved this, I got h to be equal to 46 feet.

From here I could find the adjacent side, for the purpose of checking my work, using the variable x.

tan(58*) = (58+h)/x
tan(58*) = 104/x
x=104/tan(58*)
x=64.986

For my next step, I checked my work using the trigonometric property: tan(x*) = opp/adj

tan(58*) = 1.6003
tan(58*) = (58+46)/64.986
104/64.986 = 1.6003 = tan(58*)
Therefore, h=46 feet.

Questions:
Did I do it right?
What are some other ways I could have done this?

The triangle can be divided into two right triangles with da same base or adjacent side.
One with Opposite h , and one with opposite h + 58.
Let Adjacent side be A


Tan(θ) = Opposite / Adjacent

For Smaller triangle:
Tan(46) = h / A
A = h / Tan(46)

For larger triangle
Tan(58) = (h + 58) / A
A = (h + 58) / Tan(58)

A = A , so
h / Tan(46) = (h + 58) / Tan(58)
h / (h + 58) = Tan(46) / Tan(58)
h / (h + 58) = 0.6471
h = 0.6471h + 37.53
h − 0.647h = 37.53
h = 37.53 / 0.353
[ h ≈ 106 feet ]

Hope this helps :)
Feel free 2 email me if u have any more questions !!

I cannot solve your problem either but you didn't do it right. The reason is that trigonometric ratios are not linear. For proportions to work the relationship has to be linear. The reason your problem checked is because your check assumed that you had the right answer. Your logic was circular. Frankly, I do not believe this problem can be solved. There is information missing.