Question

Your cat is stuck in a tree and you need a ladder to rescue your cat. The cat is 14 feet above the ground, and your ladder makes a 60° angle with the tree when it is long enough to reach the cat. How long is your ladder you used to rescue the cat?

Answer 1

To rescue the cat from a 14-foot height, with the ladder making a 60° angle with the ground, the ladder needs to be 28 feet long using trigonometry and the cosine function.

Step-by-step explanation:

To determine the length of the ladder needed to rescue the cat, we can use trigonometry. Since the ladder forms a 60° angle with the ground and the cat is 14 feet above the ground, we are dealing with a right triangle. We can use the cosine function, which is the adjacent side (ground to the base of the ladder) divided by the hypotenuse (length of the ladder). In this case, the length of the ladder is the hypotenuse we are trying to find.

The cosine of 60° is 0.5. If we let 'L' represent the length of the ladder, the equation is:

cos(60°) = 14 / L

Therefore:

0.5 = 14 / L

By solving for 'L', we get:

L = 14 / 0.5

L = 28 feet

The ladder used to rescue the cat must be 28 feet long.