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

1. simoner

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

2. simoner

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

3. simoner

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

4. simoner

can anyone tell me if this is correct?

5. triciaal

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6. simoner

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

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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