A 26ft ladder is placed against a vertical wall of a building, with the bottom of the ladder standing on level ground 24ft from the base of the building. How high up the wall does the ladder reach?
676-576
h =sqrt(100)
h = 10
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 is equal to the sum of the squares of the other two sides.
In this case, the ladder acts as the hypotenuse, the distance from the bottom of the ladder to the base of the building is one side, and the height up the wall is the other side.
Let's label the distance from the bottom of the ladder to the base of the building as 'a' and the height up the wall as 'b'.
According to the problem, the distance from the bottom of the ladder to the base of the building (side 'a') is 24ft. The length of the ladder (the hypotenuse) is given as 26ft.
We can use the Pythagorean theorem to solve for side 'b':
c^2 = a^2 + b^2
Where c represents the length of the hypotenuse.
In this case, c = 26ft and a = 24ft.
So, the equation becomes:
26^2 = 24^2 + b^2
Simplifying further:
676 = 576 + b^2
Subtracting 576 from both sides:
100 = b^2
Taking the square root of both sides:
√100 = √b^2
10 = b
Therefore, the ladder reaches a height of 10ft up the wall.