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) .

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=(\pi)/(6) =30`

x direction (east)

We know that ,

⇒
`cosx = (Base)/(Hypotenuse)`

⇒
`cos30 = (Base)/(13)`

⇒
`(√(3) )/(2) = (Base)/(13)`

⇒
`Base=(√(3)(13) )/(2) m`

⇒
`Base=11.2583303m`

y direction (North )

We know that ,

⇒
`sinx = (Perpendicular)/(Hypotenuse)`

⇒
`sin30 = (Perpendicular)/(13)`

⇒
`(1)/(2) = (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) .