Question

This is my next Trigonometry question I am needed help on- I just want to be sure I've got it right, or if not, then the steps I need to take to get it right. Thank you.

Answer 1

$\bf cos(\theta)=\cfrac{3}{5}\cfrac{\leftarrow adjacent=a}{\leftarrow hypotenuse=c} \\\\\\ c^2=a^2+b^2\implies \pm\sqrt{c^2-a^2}=b\implies \pm\sqrt{5^2-3^2}=b \\\\\\ \pm\sqrt{16}=b\implies \pm4=b$

so, plus or minus?  well, the angle is in the 1st quadrant, and on that quadrant, both cosine and sine are positive, so 4 = b

$\bf tan(\theta)=\cfrac{opposite}{adjacent}\implies tan(\theta)=\cfrac{4}{3}$