a cat is stuck 15 feet up in a tree.to get it down,you will place a ladder 5 feet from the base of the tree.how tall must your ladder be in order to reach the cat? Round to the nearest foot

This calls for the Pythagorean Theorem.

a^2 + b^2 = c^2

15^2 + 5^2 = c^2

15

To determine the height of the ladder needed to reach the cat, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the height of the tree is the hypotenuse, the distance from the base of the tree to the ladder (5 feet) is one side, and the unknown length of the ladder is the other side.

Let's calculate the length of the ladder using the Pythagorean theorem:

ladder^2 = tree height^2 - base distance^2

ladder^2 = 15^2 - 5^2
ladder^2 = 225 - 25
ladder^2 = 200

To find the length of the ladder, we need to take the square root of both sides:

ladder = sqrt(200)
ladder ≈ 14.14 feet

Rounding to the nearest foot, the ladder must be approximately 14 feet tall to reach the cat.

To determine how tall the ladder must be to reach the cat, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the base of the ladder is 5 feet, and the height of the tree is 15 feet. Let's call the length of the ladder "h".

According to the Pythagorean theorem:
h² = 5² + 15²
h² = 25 + 225
h² = 250

To find the value of "h", we need to take the square root of both sides of the equation:
√(h²) = √250
h = √250

Using a calculator, we find that √250 is approximately 15.81.

Since we are rounding to the nearest foot, the ladder must be about 16 feet tall in order to reach the cat.