can someone explain to me the steps from going to tan30=600sina/600cosa+600 to √3 sina= cosa +1
Do you mean this?
$\displaystyle tan(30) = \frac{600 ~ sin(a)}{600 ~ cos(a) + 600}$
Please use parenthesis where needed.
$\displaystyle tan(30) = \frac{600 \cdot sin(a)}{600 (cos(a) + 1)}$
$\displaystyle tan(30) = \frac{600}{600} \cdot \frac{sin(a)}{cos(a) + 1}$
Can you finish it?
-Dan
Note that $\tan(30^\circ)= \dfrac{1}{\sqrt{3}}$ ... you should know this because you've learned the trig values for special angles on the unit circle, correct?
Note $\dfrac{600\sin{a}}{600\cos{a}+600} = \dfrac{\sin{a}}{\cos{a}+1}$
So, your equation can be simplified to the form ...
$\dfrac{1}{\sqrt{3}}= \dfrac{\sin{a}}{\cos{a}+1}$
can you finish now?