Question

Mr. Randall is leaning a ladder against the side of his house to repair the roof. The top of the ladder reaches the roof, which is 4 meters high. The base of the ladder is 1 meter away from the house, where Mr. Randall's son is holding it steady. How long is the ladder? If necessary, round to the nearest tenth.

Answer 1

To find the length of Mr. Randall's ladder, we use the Pythagorean theorem. Considering the ladder's height of 4 meters and base of 1 meter, we calculated the ladder to be approximately 4.1 meters long after applying the theorem and rounding to the nearest tenth.

Step-by-step explanation:

To determine how long Mr. Randall's ladder is, we can use the Pythagorean theorem. This theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Here, the ladder represents the hypotenuse, the height of the roof (4 meters) is one side, and the distance from the base of the ladder to the house (1 meter) is the other side.

Following the formula:

Ladder length² = 4² + 1²
Ladder length² = 16 + 1
Ladder length² = 17

Now, take the square root of both sides to find the ladder length:

Ladder length = √17
Ladder length ≈ 4.1 meters (rounded to the nearest tenth)

Hence, the ladder is approximately 4.1 meters long.