a ladder leaning against a vertical wall has its top 8m from the level ground and whose foot is 4m from the wall.how long is the ladder?
a^2 + b^2 = c^2
8^2 + 4^2 = c^2
Take it from there.
To find the length of the ladder, we 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 ladder forms the hypotenuse of the triangle, and the vertical wall and the ground form the other two sides. Let's label the length of the ladder as 'x', the distance from the foot of the ladder to the wall as '4m', and the height of the ladder from the ground to the top as '8m'.
Using the Pythagorean theorem, the equation can be written as follows:
x^2 = 4^2 + 8^2
Simplifying the equation:
x^2 = 16 + 64
x^2 = 80
To find the value of 'x', we need to take the square root of both sides:
x = sqrt(80)
Using a calculator, we can find that:
x ≈ 8.94m
Therefore, the length of the ladder is approximately 8.94 meters.