Question

URGENT

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

r = 13 is the distance from the origin to the endpoint

theta = pi/6 radians = 30 degrees is the angle

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y = r*sin(theta)

y = 13*sin(30)

y = 13*0.5

y = 6.5

You have gone exactly 6.5 meters north.

Note: 6.5 in fraction form is 13/2; as a mixed number, it would be 6 & 1/2

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x = r*cos(theta)

x = 13*cos(30)

x = 13*sqrt(3)/2

You have gone exactly 13*sqrt(3)/2 meters to the east

Note: 13*sqrt(3)/2 = 11.25833 approximately