The straight line #y = mx# where #m > 0# forms an angle of #30^@# with the positive #x#-axis. What does #m# equal?

Question

#(A)# #sqrt3#

#(B)# #sqrt3/3#

#(C)# #2-sqrt3#

#(D)# None of the above

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Answer 1 · 2018-04-05T04:20:19

Correct answer is #sqrt(3)/3#.

(C)

By definition, #tan(theta)=sin(theta)/cos( theta)#.
#sin(theta)# is the y-component in the unit circle and #cos(theta)# the x component.

Therefore #tan(theta) = y/x# or the slope of the line.

Since the angle is 30 degrees, #tan(30)=m#. #tan(30°) = 1/sqrt(3)#.

Rationalize: #1/sqrt(3)*sqrt(3)/sqrt(3)# to get #sqrt(3)/3#.