a 14 foot ladder placed against a vertical wall of a building with the bottom of the ladder standing on level ground 9 feet from the base of the building. how high up the wall does the ladder reach?
simple application of Pythagoras ...
h^2 + 9^2 = 14^
solve for h
Very poor and unsafe placement of a ladder !!!!
To determine how high up the wall the ladder reaches, 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 ladder is the hypotenuse, and the horizontal distance from the wall to the base of the ladder is one of the other two sides. Let's call this distance "x". The vertical distance from the base of the wall to the top of the ladder is the second side, which we'll call "h".
According to the given information, the ladder is 14 feet long, and the horizontal distance from the wall to the base of the ladder is 9 feet.
Using the Pythagorean Theorem:
14^2 = 9^2 + h^2
Simplifying the equation:
196 = 81 + h^2
To solve for h^2, subtract 81 from both sides:
h^2 = 115
Now, we can solve for h by taking the square root of both sides:
h = √115
h ≈ 10.72
Therefore, the ladder reaches approximately 10.72 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 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 acts as the hypotenuse, and the distance from the base of the building to the bottom of the ladder is one side of the right triangle, while the height up the wall is the other side.
Let's call the height up the wall "h". So, according to the Pythagorean theorem:
(9 feet)^2 + h^2 = (14 feet)^2
Simplifying this equation, we have:
81 + h^2 = 196
Subtracting 81 from both sides, we get:
h^2 = 196 - 81
h^2 = 115
To solve for h, we take the square root of both sides:
√(h^2) = √115
h = √115
Therefore, the ladder reaches approximately 10.72 feet up the wall.