A 20 foot ladder is leaning against the side of a building. The bottom of the ladder is 4 feet from the wall. How many feet above the ground does the ladder touch the wall?
The ladder, the ground, and the wall make a right triangle. Use the pythagorean theorem to find the height.
a^2 + b^2 = c^2
a^2 + 4^2 = 20^2
a^2 + 16 = 400
a^2 = 384
a = 19.5959
16
Well, with a 20-foot ladder and a 4-foot distance from the wall, we can think of it as a "wall-measuring ladder." So, we'll subtract the 4 feet from the 20 feet and voila! The ladder touches the wall approximately 16 feet above the ground. It's quite the high-flying ladder!
To determine how many feet above the ground the ladder touches the wall, we can use the Pythagorean theorem.
According to the theorem, the square of the length of the ladder (hypotenuse) is equal to the sum of the squares of the other two sides. In this case, the ladder is the hypotenuse, and the distances from the wall to the ladder and from the ground to the ladder are the other two sides.
Let's calculate:
The distance from the wall to the ladder is given as 4 feet.
The length of the ladder is given as 20 feet.
Using the Pythagorean theorem:
Length of the ladder squared = Distance from the wall squared + Distance from the ground squared.
So, 20 feet ladder squared = 4 feet distance from the wall squared + Distance from the ground squared.
400 feet squared = 16 feet squared + Distance from the ground squared.
Rearranging the equation, we get: Distance from the ground squared = 400 feet squared - 16 feet squared.
This simplifies to: Distance from the ground squared = 384 feet squared.
Now, calculating the square root of both sides to find the Distance from the ground:
Distance from the ground = √(384 feet squared).
Distance from the ground ≈ 19.60 feet.
Therefore, the ladder touches the wall approximately 19.60 feet above the ground.
To find out how many feet above the ground the ladder touches the wall, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right 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 represents the hypotenuse, and the distance between the bottom of the ladder and the wall represents one of the other two sides. Let's call this side "a". The height above the ground that the ladder touches the wall represents the remaining side. Let's call this side "b".
According to the Pythagorean theorem, we have:
a^2 + b^2 = c^2
where a = 4 feet (distance from the bottom of the ladder to the wall) and c = 20 feet (length of the ladder).
We can plug in these values and solve for b:
4^2 + b^2 = 20^2
16 + b^2 = 400
b^2 = 400 - 16
b^2 = 384
To find the value of b, we need to take the square root of both sides:
b = sqrt(384)
b ≈ 19.6 feet
Therefore, the ladder touches the wall at approximately 19.6 feet above the ground.