a ladder 26m long leans against a wall. The top of the ladder from the ground is 24m. What is the length of the base resting on the level ground from the wall
Answer
a = 24
b = ?
c = 26
Use the Pythagorean Theorem.
a^2 + b^2 = c^2
To find the length of the base resting on the level ground from the wall, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square 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 a right-angled triangle with the wall and the ground. The length of the ladder (hypotenuse) is 26m, and the height of the ladder from the ground to the top is 24m.
Using the Pythagorean theorem, we can calculate the length of the base of the ladder on the ground. Let's call it "x":
x^2 + 24^2 = 26^2
Simplifying the equation:
x^2 + 576 = 676
Subtracting 576 from both sides:
x^2 = 100
Taking the square root of both sides:
x = √100
x = 10
Therefore, the length of the base of the ladder resting on the level ground from the wall is 10 meters.
To find the length of the base resting on the level ground from the wall, we will use the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, one side is the height of the ladder from the ground (24m), and the other side is the length of the base resting on the level ground that we need to find (let's call it x).
So, using the Pythagorean theorem, we have the equation:
ladder^2 = height^2 + base^2
26^2 = 24^2 + x^2
Simplifying the equation, we get:
676 = 576 + x^2
Subtracting 576 from both sides, we have:
x^2 = 100
Taking the square root of both sides, we get:
x = 10
Therefore, the length of the base resting on the level ground from the wall is 10 meters.