i cant find $\tan\theta$ i think i need to use ratios or similarity some how

Question

if you can help me with finding $\tan(\theta)$ it would help me a lot, as I wanna know how to do it and what identities to use, possibly triangle similarities or something to do with ratios question #9 is the problem.

Answer 1

Hints:

1) If $\tan \theta = \dfrac 4 3,$ $\sin \theta = ?$ and $\cos \theta = ?$ by the Pythagorean theorem?

2) $\cot \dfrac \theta 2 = \csc \theta + \cot \theta$ or $\dfrac {1+ \cos\theta}{\sin \theta}$; use the results you found in Hint #1.