Question

To wash a window that is 30 feet off the ground, Lacey leans a 34-foot ladder against the side of the building. To reach the window, how far away from the building should Lacey place the base of the ladder?

a) 3 feet
b) 4 feet
c) 5 feet
d) 6 feet

Answer 1

Lacey should place the base of the 34-foot ladder 16 feet away from the building to reach a window that is 30 feet off the ground, as calculated using the Pythagorean Theorem.

Step-by-step explanation:

To determine how far away from the building Lacey should place the base of the ladder to reach a window that is 30 feet off the ground using a 34-foot ladder, we can use the Pythagorean Theorem. The ladder, the distance from the building, and the height she needs to reach form a right-angled triangle. According to the theorem, the sum of the squares of the two shorter sides (base and height) is equal to the square of the longest side (the hypotenuse, which in this case is the ladder).

The formula is: Base2 + Height2 = Hypotenuse2.

Plugging in the values:

Base2 + 302 = 342

Base2 + 900 = 1156

Base2 = 1156 - 900

Base2 = 256

Base = √256

Base = 16

Therefore, Lacey should place the base of the ladder 16 feet away from the building to safely reach the window.