Answer:
[tex]\frac{-1}{\sqrt{17} }[/tex]
Step-by-step explanation
We have given that equation of line a+4b=0
⇒4b= -a
⇒[tex]b= \frac{-a}{4}[/tex]
slope of line = [tex]tan\theta =\frac{P}{B}= \frac{-1}{4}[/tex]
⇒ [tex]tan\theta[/tex] is negative therefore it lies into 4th quadrant
By, Pythagoras theorem [tex]H^2=P^2+B^2[/tex]
by putting value of P= -1 & B=4
the value of [tex]H=\sqrt{17}[/tex]
with the given condition [tex]cos\theta>0 [/tex]
i.e. [tex]\theta[/tex]∈ (3π/2, 2π)
now, [tex]sin\theta= \frac{P}{H}= \frac{-1}{\sqrt{17}}[/tex]
