Physics
posted by Leanna .
A 23 kg child goes down a straight slide inclined 38 degrees above horizontal. The child is acted on by his weight, the normal force from the slide, and kinetic friction.

(23kg)(9.8m/s^2)(cos(38)) = 177.6N

You do not say if the child is going at constant speed or alternatively what the coef of friction is. You also do not say what the question is.

All I can say is
normal force = 23 * 9.81 * cos 38 = 178 N agreed
force down slide = 23 * 9.81 * sin 38 = 139 N
force up slide = 178 * mu
so
23 a = 139  178 mu
if a = zero, you can solve for mu
if you know mu, you can solve for a 
The normal force is 160 N. I am not quite sure how to find it though. The back of my textbook just says 160 N.