What Does X Need To Be Such That It Produces An Acceleration Of 5.6 M/s2 Down The Incline?

The force on the mass due to gravity (F_g=m*g) can be resolved into two perpendicular forces, one along the length of the plane, and the other normal to it. The magnitudes of each of these are F_gsine[x] and F_gcosine[x], respectively.

So, the acceleration down the incline is
F_gsine[x] = m*a = m(5.6 meters/sec²)
m*g*sine[x] = m*(5.6 meters/sec²)
m*(9.8 meters/sec²)*sine[x] = m*(5.6 meters/sec²)

Pay attention. Here, we're going to divide out mass "m" from both sides, and begin using "m" for "meters" as in "meters/sec²".

(9.8 m/s²)*sine[x] = 5.6 m/s²
sine[x] = (5.6 m/s²)/(9.8 m/s²)    (divide both sides by 9.8)
x = arcsine[ (5.6 m/s²)/(9.8 m/s²)]    (take the arcsine of both sides)
 = arcsine[5.6/9.8]    (cancel the units)
 = arcsine[.428571] = 34.85^o.    (I use the underline to indicate a repeating decimal. Usually an overbar is used, but I don't know how to create that.)

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