Question

Why did I get different answers to find x?

Answer 1

$\bf tan(39^o)=\cfrac{\stackrel{opposite}{x}}{\stackrel{adjacent}{8}}\implies 8\cdot tan(39^o)=x\implies 6.48\approx x \\\\[-0.35em] ~\dotfill\\\\ \cfrac{sin(39^o)}{x}=\cfrac{sin(51^o)}{8}\implies \cfrac{8\cdot sin(39^o)}{sin(51^o)}=x\implies 6.48\approx x$

one thing to bear in mind is that calculators have two modes, Degree mode and Radian mode, if your calculator is in Radian mode and you plug in tan(39), it thinks "tangent of 39 radians" and so it gives that, bearing in mind that 1 radian is about 57°.

So make if you're using degrees as the angle, make sure your calculator is in Degree mode first, thus tan(39) will mean "tangent of 39 degrees".

$\bf 8\cdot tan(39~rad) \approx 28.9~\hspace{10em} \cfrac{8\cdot sin(39~rad)}{sin(51~rad)}\approx 11.5$