Answer :
Line goes 11.2583303 meters in the x direction (east) and 7.5 meters in the y direction (north) .
Step-by-step explanation:
Here we have , If I have a line that starts at the origin (0,0), and goes 13 meters at an angle of π/6 in the standard position (i.e. 30° north of east) . We need yo find how far does it go in the y direction (north), and how far does it go in the x direction (east). Let's find out:
According to question we have a right angle triangle as :
[tex]Hypotenuse =13m\\x=\frac{\pi}{6} =30[/tex]
x direction (east)
We know that ,
⇒ [tex]cosx = \frac{Base}{Hypotenuse}[/tex]
⇒ [tex]cos30 = \frac{Base}{13}[/tex]
⇒ [tex]\frac{\sqrt{3} }{2} = \frac{Base}{13}[/tex]
⇒ [tex]Base=\frac{\sqrt{3}(13) }{2} m[/tex]
⇒ [tex]Base=11.2583303m[/tex]
y direction (North )
We know that ,
⇒ [tex]sinx = \frac{Perpendicular}{Hypotenuse}[/tex]
⇒ [tex]sin30 = \frac{Perpendicular}{13}[/tex]
⇒ [tex]\frac{1}{2} = \frac{Perpendicular}{13}[/tex]
⇒ [tex]Perpendicular=7.5m[/tex]
Therefore , Line goes 11.2583303 meters in the x direction (east) and 7.5 meters in the y direction (north) .