Question

Right triangle question ​

Answer 1

You can use the sine law to state that

$\dfrac{r}{\sin(y)}=\dfrac{q}{\sin(x)}$

We can rearrange this equation into

$\dfrac{r}{q}=\dfrac{\sin(y)}{\sin(x)}$

Now, since this is a right triangle, we have

$x=90-y$

which implies

$\sin(x)=\sin(90-y)=\cos(y)$

And so we have

$\dfrac{r}{q}=\dfrac{\sin(y)}{\sin(x)} = \dfrac{\sin(y)}{\cos(y)}=\tan(y)$