A ladder 6m long is placed against a vertical wall,its lower end is 2m away from the wall. How high up the wall does it reach?give your answer in one decimal place.
recall the distance formula:
2^2 + h^2 = 6^2
i want to see answers
I dont know
To find out how high the ladder reaches up the wall, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In this case, the ladder forms the hypotenuse, and the distance from the bottom of the ladder to the wall represents one of the sides, while the height we want to find represents the other side.
Let's denote the height of the ladder up the wall as h. According to the problem, the distance from the bottom of the ladder to the wall is given as 2m, and the length of the ladder is given as 6m.
Using the Pythagorean theorem, we have:
h^2 + 2^2 = 6^2
Simplifying the equation:
h^2 + 4 = 36
Subtracting 4 from both sides:
h^2 = 32
Take the square root of both sides to solve for h:
h = √32
Calculating the square root of 32:
h ≈ 5.7
Therefore, the ladder reaches approximately 5.7m up the wall.