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?

Answer 1

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.