User:CNSW

We know for all right triangles that:

$$ \sin x = \left ( \frac{opp}{hyp} \right ) $$

$$ \tan x = \left ( \frac{opp}{adj} \right ) $$

From the latter we can deduce

$$ \tan x \times adj = opp $$

Through substitution into our first equation, it follows that

$$ \sin x = \left ( \frac{\tan x \times adj}{hyp} \right ) $$

And through standard algebra:

$$ \sin x \times hyp = \tan x \times adj $$

$$ \tan x = \left ( \frac{\sin x \times hyp}{adj} \right ) $$

Substitute that back into $$\sin x = \left ( \frac{\tan x \times adj}{hyp} \right )$$