Chapter 7 - Applications of Trigonometry and Vectors - Summary Exercises on Applications of Trigonometry and Vectors - Page 345: 5

Mary must apply a force of 42 lb.

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