A ladder is propped against a wall. If the top of the ladder reaches 18 feet up the wall and the base of the ladder is 6 feet from the base of the wall, how long is the ladder?
If you sketch this out, the ladder, up against the wall, forms right triangle.
Using the Pythagorean theorem, you need to find c, the hypotenuse.
c^2 = 6^2 + 18^2
Solve for c, the length of the ladder.
129600
To find the length of the ladder, we can use the Pythagorean theorem, which states that the square of the hypotenuse (length of the ladder) is equal to the sum of the squares of the other two sides. In this case, the ladder is the hypotenuse, and the height of the wall and the distance from the wall to the base of the ladder form the other two sides.
Let's represent the length of the ladder as 'L', the height of the wall as 'H', and the distance from the wall to the base of the ladder as 'D'.
Using the Pythagorean theorem, we have:
L^2 = H^2 + D^2
Substituting the given values, we get:
L^2 = 18^2 + 6^2
L^2 = 324 + 36
L^2 = 360
Taking the square root of both sides, we find:
L = √360
L ≈ 18.97 feet (rounded to two decimal places)
Therefore, the length of the ladder is approximately 18.97 feet.
To find the length of the ladder, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length 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 a right triangle with the wall and the ground:
So, the ladder acts as the hypotenuse of the triangle, which we'll call 'c'. The height of the wall is one side of the triangle, called 'a', and the length from the base of the wall to the ladder contact point on the ground is the other side, called 'b'.
According to the Pythagorean theorem, we have the equation:
c^2 = a^2 + b^2
In this case, we know that 'a' (the height of the wall) is 18 feet, and 'b' (the distance from the base of the wall to the ladder's contact point on the ground) is 6 feet.
Plugging in these values, we have:
c^2 = 18^2 + 6^2
Simplifying, we get:
c^2 = 324 + 36
c^2 = 360
To find the length of the ladder, we take the square root of both sides:
√c^2 = √360
c = √360
Calculating this, we find that the length of the ladder is approximately 18.97 feet, rounded to two decimal places.