Answer
The hill makes an angle of $18.2^{\circ}$ with the horizontal.
Work Step by Step
The crate's weight of $80~lb$ is directed straight down. The force of $25~lb$ is directed up the hill at an angle of $\theta$ above the horizontal.
We can draw a right angle triangle with the $80~lb$ as the hypotenuse of the triangle and the force of $25~lb$ opposite the angle $\theta$.
We can find $\theta$:
$sin~\theta = \frac{25}{80}$
$\theta = arcsin(\frac{25}{80})$
$\theta = 18.2^{\circ}$
The hill makes an angle of $18.2^{\circ}$ with the horizontal.
