the angle between two straight lines

Question

if the angle between two straight lines L1 and L2 is 45 degree and the slope of L2 IS -5 find the slope of L1

Answer 1

We will need the trig identity tan(A+B)=(tanA+tanB)/(1-tanAtanB).

We also need to remember that tan45=1 or 45=arctan(1).

Let the slope of L1 be m1 and the slope of L2 be m2, then:

arctan(m1)-arctan(m2)=45, the angle between the lines.

So arctan(m1)=45+arctan(m2) and:

m1=tan(45+arctan(m2))=tan(arctan(1)+arctan(m2)).

m2=-5. Remember that tan(arctan(x))=x.

Now apply the trig identity:

m1=(1-5)/(1+5)=-4/6=-⅔. So the slope of L1 is -⅔.