10. A ladder leaning against a vertical wall is 11.28 m high up against the wall. The foot of the ladder is 5m from the wall. Calculate the length of the ladder.
To find the length of the ladder, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the square of the other two sides.
In this case, the height of the ladder against the wall is one side of the right triangle, and the distance from the wall to the foot of the ladder is the other side. The length of the ladder is the hypotenuse.
Let's call the length of the ladder "L".
According to the Pythagorean theorem, we have:
L^2 = (11.28)^2 + (5)^2
L^2 = 127.2384 + 25
L^2 = 152.2384
Taking the square root of both sides, we get:
L = √152.2384
L ≈ 12.33
Therefore, the length of the ladder is approximately 12.33 meters.
To calculate the length of the ladder, you can 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 wall, the floor, and the ladder form a right-angled triangle, with the ladder being the hypotenuse. The height of the wall is given as 11.28 m and the distance from the foot of the ladder to the wall is given as 5 m.
Using the Pythagorean theorem, we can set up the following equation:
Ladder^2 = Height^2 + Distance^2
Substituting the given values, we get:
Ladder^2 = 11.28^2 + 5^2
Ladder^2 = 127.2384 + 25
Ladder^2 = 152.2384
Taking the square root of both sides, we find:
Ladder ≈ √152.2384
Ladder ≈ 12.34 m
Therefore, the length of the ladder is approximately 12.34 meters.
recall the Pythagorean Theorem. If the ladder length is z, then
11.28^2 + 5^2 = z^2