A 19
-foot
ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 12
feet from the base of the building. How high up the wall does the ladder reach?
We can use the Pythagorean Theorem to solve this problem. Let's label the height up the wall that the ladder reaches as "h". Then, we have:
h^2 + 12^2 = 19^2
Simplifying this equation, we get:
h^2 + 144 = 361
Subtracting 144 from both sides, we get:
h^2 = 217
Taking the square root of both sides, we get:
h = sqrt(217)
This is approximately equal to 14.73 feet. Therefore, the ladder reaches approximately 14.73 feet up the wall.
To find out how high up the wall the ladder reaches, we can use the Pythagorean theorem. The Pythagorean theorem 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 is the hypotenuse, and the distance from the base of the building to the ladder's bottom is one of the legs of the triangle.
Given:
Length of the ladder (hypotenuse) = 19 feet
Distance from the base of the building to the ladder's bottom (one leg) = 12 feet
Let's call the height up the wall that the ladder reaches 'x' feet.
Using the Pythagorean theorem, we have:
(12^2) + (x^2) = (19^2)
144 + x^2 = 361
Now, we can solve for 'x':
x^2 = 361 - 144
x^2 = 217
Taking the square root of both sides, we get:
x = √217
So, the ladder reaches approximately √217 feet up the wall.