Question

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 (ie. 30° north of east) how far does it go in the y direction (north), and how far does it go in the x direction (east)? Give exact values.

Answer 1

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 :

$Hypotenuse =13m\\x=\frac{\pi}{6} =30$

x direction (east)

We know that ,

⇒ $cosx = \frac{Base}{Hypotenuse}$

⇒ $cos30 = \frac{Base}{13}$

⇒ $\frac{\sqrt{3} }{2} = \frac{Base}{13}$

⇒ $Base=\frac{\sqrt{3}(13) }{2} m$

⇒ $Base=11.2583303m$

y direction (North )

We know that ,

⇒ $sinx = \frac{Perpendicular}{Hypotenuse}$

⇒ $sin30 = \frac{Perpendicular}{13}$

⇒ $\frac{1}{2} = \frac{Perpendicular}{13}$

⇒ $Perpendicular=7.5m$

Therefore , Line goes 11.2583303 meters in the x direction (east) and 7.5 meters in the y direction (north) .