A 25 foot ladder is leaned against the wall. If the base of the ladder is 7 feet from the wall, how high up the wall, will the ladder reach?
We can use the Pythagorean theorem to solve this problem.
Let's use the variables a and b to represent the height up the wall and the distance along the ground, respectively. The length of the ladder, represented by c, is given as 25 feet.
According to the Pythagorean theorem, the sum of the squares of the lengths of the two legs (a and b) is equal to the square of the length of the hypotenuse (c). In this case, we have:
a^2 + b^2 = c^2
Substituting in the known values, we have:
a^2 + 7^2 = 25^2
a^2 + 49 = 625
a^2 = 625 - 49
a^2 = 576
Taking the square root of both sides, we find:
a = √576
a = 24
Therefore, the ladder will reach 24 feet up the wall.
To find out how high up the wall the ladder will reach, we can use the Pythagorean theorem which states that the square of the hypotenuse (the longest side) of a right triangle is equal to the sum of the squares of the other two sides.
In this scenario, the ladder acts as the hypotenuse of a right triangle, with one side being the distance from the base of the ladder to the wall, and the other side being the height up the wall the ladder reaches.
Given:
Base of the ladder: 7 feet
Length of the ladder (hypotenuse): 25 feet
Let's denote the height up the wall the ladder reaches as 'x'.
Using the Pythagorean theorem, we have:
(7)^2 + (x)^2 = (25)^2
Simplifying the equation, we get:
49 + x^2 = 625
Subtracting 49 from both sides, we have:
x^2 = 625 - 49
x^2 = 576
Now, taking the square root of both sides, we get:
x = sqrt(576)
x ≈ 24
Therefore, the ladder will reach a height of approximately 24 feet up the wall.