If you place a 35-foot ladder against the top of a 31-foot building, how many feet will the bottom of the ladder be from the bottom of the building? Round to the nearest tenth of a foot.
We can use the Pythagorean theorem to solve this problem. Let x be the distance from the bottom of the building to the bottom of the ladder. Then we have:
x^2 + 31^2 = 35^2
Simplifying the right side, we get:
x^2 + 961 = 1225
Subtracting 961 from both sides, we get:
x^2 = 264
Taking the square root of both sides, we get:
x ≈ 16.2
Rounding to the nearest tenth of a foot, we get:
x ≈ 16.2 feet
Therefore, the bottom of the ladder will be about 16.2 feet from the bottom of the building.
To solve this question, we can use the Pythagorean theorem, which 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 scenario, the ladder is the hypotenuse, and the building and the distance from the bottom of the ladder to the bottom of the building form the other two sides of the right triangle.
Let's label the distance from the bottom of the ladder to the bottom of the building as 'x'.
According to the Pythagorean theorem:
(length of ladder)^2 = (length of building)^2 + (distance from bottom of ladder to the bottom of the building)^2
(35)^2 = (31)^2 + x^2
1225 = 961 + x^2
Subtracting 961 from both sides:
1225 - 961 = x^2
264 = x^2
To solve for x, we need to take the square root of both sides:
sqrt(264) = sqrt(x^2)
16.248 = x
Rounded to the nearest tenth, the bottom of the ladder will be approximately 16.2 feet from the bottom of the building.