Question

John is hanging some lights around his house for the holidays. However, there are bushes around the house, so the bottom of his extension ladder can only be placed as close as 33​ feet away from his house. If he wants the ladder to reach a height 44​ feet above the ground, how long should the ladder be, in feet?

Answer 1

55.0

Explanation:

To find the length of the ladder, we can use the Pythagorean theorem, which states that for any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs¹.

In this case, the ladder forms a right triangle with the ground and the wall, where the ladder is the hypotenuse and the distance from the house and the height of the ladder are the legs. We can label these lengths as follows:

- c = length of ladder (hypotenuse)

- a = distance from house (leg)

- b = height of ladder (leg)

Using the Pythagorean theorem, we can write:

$$c^2 = a^2 + b^2$$

We are given that a = 33 feet and b = 44 feet, so we can plug in these values and solve for c:

$$c^2 = 33^2 + 44^2$$

$$c^2 = 1089 + 1936$$

$$c^2 = 3025$$

$$c = \sqrt{3025}$$

$$c \approx 55.0$$

Therefore, the length of the ladder should be about **55.0 feet**.

S