Two roommates are moving a couch from the first floor to the second floor of their apartment. They each lift one end of the couch and carry it level across the first floor, so that they each apply a force equal to half the weight of the couch. The roommate in the lead reaches the stairs and walks up several steps to a point where they are standing $4\mathrm{.}97$ feet above the first floor, while the other roommate is still standing on the floor. The couch is $8\mathrm{.}00$ feet long and weighs $160$ pounds. The force exerted on the couch by the lead roommate is perpendicular to the bottom of the couch, but the force exerted by the other roommate is not. Find:

$($a$)$ the magnitude of the force exerted by the lead roommate on the couch;

$($b$)$ the magnitude of the force exerted by the other roommate on the couch.