$\"\"$

\

Draw the related diagram :

\

$\"\"$ $\"\"$

\

Observe the diagram: \ \

\

The force required to keep sienna from rolling down the hill is $\"\"$ .

\

The magnitude of the force perpendicular to the hill is $\"\"$ .

\

The force $\"\"$ .

\

$\"\"$

\

Consider the subpart from the diagram.

\

$\"\"$

\

The weight is $\"\"$ .

\

From the figure :

\

$\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Therefore, the force required to keep sienna from rolling down the hill is $\"\"$ .

\

Consider $\"\"$

\

Substitute $\"\"$ .

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The magnitude of the force perpendicular to the hill is $\"\"$ .

\

$\"\"$

\

The force required to keep sienna from rolling down the hill is $\"\"$ .

\

The magnitude of the force perpendicular to the hill is $\"\"$ .