So, we have found that the magnitude of the component of force along the lawnmower's displacement is equal to the magnitude of the total force exerted by the man on the lawnmower multiplied by cosine theta, where theta is the angle between the force exerted by the man and the displacement of the lawnmower. Now, we just need to plug this into our equation for work, which says work is equal to the magnitude of the component of force along displacement multiplied by displacement.
See the image at the right. |

After simplification, we find that the work done by the man on the lawnmower is equal to the magnitude of the force exerted by the man on the lawnmower multiplied by the displacement of the lawnmower multiplied by cosine theta, where theta is the angle between the force exerted by the man and the displacement of the lawnmower.

*See the image above.*