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  • 24-07-2019
  • Mathematics
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Right triangle question ​

Right triangle question class=

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Аноним Аноним
  • 24-07-2019

You can use the sine law to state that

[tex]\dfrac{r}{\sin(y)}=\dfrac{q}{\sin(x)}[/tex]

We can rearrange this equation into

[tex]\dfrac{r}{q}=\dfrac{\sin(y)}{\sin(x)}[/tex]

Now, since this is a right triangle, we have

[tex]x=90-y[/tex]

which implies

[tex]\sin(x)=\sin(90-y)=\cos(y)[/tex]

And so we have

[tex]\dfrac{r}{q}=\dfrac{\sin(y)}{\sin(x)} = \dfrac{\sin(y)}{\cos(y)}=\tan(y)[/tex]

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