#### Answer

A force of $34~lb$ keeps the sled from sliding down.

#### Work Step by Step

Let $F$ be the force directed up the incline that keeps the sled from sliding down.
The sled's weight of $75~lb$ is directed straight down. The force $F$ is directed up the incline at an angle of $27^{\circ}$ above the horizontal.
We can draw a triangle with the $75~lb$ as the hypotenuse of the triangle and the force $F$ opposite the angle of $27^{\circ}$.
We can find the force $F$:
$\frac{F}{75~lb} = sin~27^{\circ}$
$F = (75~lb)~sin~27^{\circ}$
$F = 34~lb$
A force of $34~lb$ keeps the sled from sliding down.