Isabels weight is the force exerted due to gravity, .

To find the force required to keep her from sliding down the slope, project onto a unit vector in the direction of the side of the hill.

Find a unit vector in the direction of the side of the hill.

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Find , the projection of onto the unit vector , .

Projection of onto : .

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Since points down the hill, the force required is .

Since is a unit vector, represents the magnitude of the force required to keep Isabel from sliding down the slide.

The magnitude of the force required to keep Isabel from sliding down the slide is .