Mr. Peterson is leaning a ladder against the side of his house to repair the roof. The top of the ladder reaches the roof, which is 6 meters high. The base of the ladder is 5 meters away from the house, where Mr. Peterson's son is holding it steady. How long is the ladder? If necessary, round to the nearest tenth.
Question
Mr. Peterson is leaning a ladder against the side of his house to repair the roof. The top of the ladder reaches the roof, which is 6 meters high. The base of the ladder is 5 meters away from the house, where Mr. Peterson's son is holding it steady. How long is the ladder? If necessary, round to the nearest tenth.
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: a² + b² = c².
In this case, the height of the house is one side of the triangle (a), the distance from the base of the ladder to the house is the other side (b), and the length of the ladder is the hypotenuse (c). We are trying to find c.
Given: a = 6 meters (height of the house) b = 5 meters (distance from the base of the ladder to the house)
We can substitute these values into the Pythagorean theorem:
(6m)² + (5m)² = c² 36m² + 25m² = c² 61m² = c²
To find c, we take the square root of both sides:
c = √61m² c = 7.81 meters
So, the length of the ladder is approximately 7.8 meters when rounded to the nearest tenth.
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