Mr. Harvey is leaning a ladder against the side of his house to repair the roof. The top of the ladder reaches the roof, which is 5 meters high. The base of the ladder is 5 meters away from the house, where Mr. Harvey's son is holding it steady. How long is the ladder? If necessary, round to the nearest tenth. meters
Question
Mr. Harvey is leaning a ladder against the side of his house to repair the roof. The top of the ladder reaches the roof, which is 5 meters high. The base of the ladder is 5 meters away from the house, where Mr. Harvey's son is holding it steady. How long is the ladder? If necessary, round to the nearest tenth. meters
Solution
To solve this problem, we can use the Pythagorean theorem, which states that in a right 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. This can be written as a^2 + b^2 = c^2, where c represents the length of the hypotenuse, and a and b represent the lengths of the other two sides.
In this case, the height of the house represents one side of the triangle (a), the distance from the base of the ladder to the house represents the other side (b), and the length of the ladder represents the hypotenuse (c). We are given that a = 5 meters and b = 5 meters, and we are asked to find c.
Substituting the given values into the Pythagorean theorem, we get:
5^2 + 5^2 = c^2 25 + 25 = c^2 50 = c^2
To find c, we take the square root of both sides of the equation:
c = sqrt(50) ≈ 7.1 meters
So, the ladder is approximately 7.1 meters long.
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