#### Answer

Mary must apply a force of 42 lb.

#### Work Step by Step

Let $a, b$, and $c$ be vectors.
Let $a$ be the horizontal force that Mary applies.
Let $b$ be Brittany's weight.
Let $c$ be the force of the swing's rope.
Let $d = -c$
Then: vector a + vector b = vector d
Note that these three vectors form a right triangle.
We can find the magnitude of $a$:
$\frac{a}{b} = tan~40^{\circ}$
$a = b~tan~40^{\circ}$
$a = (50~lb)~tan~40^{\circ}$
$a = 42~lb$
Mary must apply a force of 42 lb