What is the ratio of $\tan 37° / \tan 54°$?

Question

I was asked this question in my class test with the following choices.

Ratio of $\tan 37° / \tan 54°$

$ 1) 3^2 : 4^2 $
$ 2) 4 : 3$
$ 3) \sqrt 3 : 2 $
$ 4) \sqrt 3 : 1 $

I was not given any tables. How to find the values?

Answer 1

Whoever wrote this class test is being very unhelpful. They actually want the ratio of

$$\frac{\tan(36.86989765...)}{\tan(53.13010235...)}$$

And that is $$\frac {\tan(\arctan(\frac34))}{\tan(\arctan(\frac43))}=\frac {9}{16}$$

So the ratio is $3^2:4^2$