## anonymous one year ago find the acute angle between the lines x+2y=7 and 5x-y=2

1. anonymous

I did$\tan^{-1} \left( 5 \right)=78.69 degrees$

2. anonymous

and $\tan^{-1} \left( -.5 \right)=-26.75 degrees$ so arent yu supposed to subtract that from 180 to get 153.43 degrees

3. anonymous

then you subtract 153.43 degrees from 78.69 degrees to get 75.74 degrees?

4. anonymous

can anyone tell me if this is correct?

5. triciaal

|dw:1440901646597:dw|

6. anonymous

is what i did correct? i just need to know if the answer i got is correct

7. triciaal

I don't know sorry but the intersection is (1,3)

8. triciaal

|dw:1440902711014:dw|

9. anonymous

2y=-x+7 $y=-\frac{ 1 }{ 2 }x+\frac{ 7 }{ 2 }$ slope$m _{1}=-\frac{ 1 }{ 2 }$ y=5x-7 its slope$m _{2}=5$ let theta be the angle between them. $\tan \theta =\left| \frac{ m _{1}-m _{2} }{ 1+m _{1}m _{2} } \right|$ $\tan \theta=\left| \frac{ -\frac{ 1 }{ 2 }-5 }{ 1+\left( -\frac{ 1 }{ 2 } \right)*5 } \right|$ $\tan \theta=\left| \frac{ \frac{ -11 }{ 2 } }{ 1-\frac{ 5 }{ 2 } } \right|=\left|\frac{ -11 }{ 2 }\times \frac{ -2 }{ 3 } \right|$ $=\frac{ 11 }{ 3 }$ $\theta=\tan^{-1} \left( \frac{ 11 }{ 3 } \right)$ =74.74degree

10. triciaal

interesting 72, 75, 78 as in 75 +/- 3

11. anonymous

correction y=5x-2