## anonymous 4 years ago wt

1. anonymous

it is easiest to do it with a picture of a triangle |dw:1354676626218:dw|

2. anonymous

that is a picture of a triangle with angle $$x$$ and with $$\tan(x)=2$$ so $$x=\arctan(2)$$ and you are looking for $$\sin(\arctan(2))=\sin(\arctan(x))$$ to find it you need the hypotenuse of the triangle. by pythagoras it is $\sqrt{2^2+1^2}=\sqrt{5}$

3. anonymous

sorry i meant you are looking for $$\sin(x)$$

4. anonymous

now we have completed the triangle |dw:1354676824808:dw|

5. anonymous

and $$\sin(x)=\sin(\arctan(2))=\frac{2}{\sqrt{5}}$$

6. anonymous