Scale math font with newtxsf

I’m using uarial as text font and want to use newtxsf as a nearly matching math font. I scaled uarial to match the height of latin modern as described in this post: https://tex.stackexchange.com/a/206677.

Still I’m encountering two problems:

• I don’t know how to scale newtxsf correctly, since theht0 stays the same when I change the scaled option. If there is no way to display the height directly I would try some values and choose the one that fits the most.
• in math mode, "sin", "cos", … are not set in uarial but in latin modern. Is there a way to tell newtxsf to use sffamily instead of rmfamily? I tried to solve this using the newtxsf documentation but failed. Or is there another package that matched uarial?

My Code so far

documentclass[fontsize=12pt, paper=a4, parskip=half]{scrreprt}
usepackage[utf8]{inputenc}
usepackage[T1]{fontenc}
usepackage{lmodern}
usepackage[scale=0.93]{tgheros}
usepackage[scaled=1]{newtxsf}
 
renewcommand*{familydefault}{sfdefault}

begin{document}
    textbf{Displaying height of fonts}par
    sbox0{sffamily A}heros: theht0 
    sbox0{rmfamily A}latin modern: theht0
    sbox0{ttfamily A}newtxsf: theht0par
    textbf{Math mode}  $ Q = Ptan(varphi)$
end{document}

Compiled Document:

documentclass[fontsize=12pt, paper=a4]{scrreprt}
usepackage[utf8]{inputenc}
usepackage[T1]{fontenc}
usepackage{amsmath}
usepackage[scale=.91757]{tgheros}
usepackage[scaled=1]{newtxsf}

renewcommand*{familydefault}{sfdefault}
renewcommand*{rmdefault}{sfdefault}

% this to get the operators in the sans serif font
DeclareSymbolFont{operators}{encodingdefault}{sfdefault}{m}{n}

begin{document}

    textbf{Displaying height of fonts}

    sbox0{sffamily A}heros: theht0

    sbox0{$A$}newtxsf: theht0

    textbf{Math mode}  $ Q = Ptan(varphi)$

end{document}