Use the Pythagorean Theorem Practice

Question

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Question
Camila needs to fix the window on the front of her house. The bottom of the window is 16 ft. from the ground. She only has a 20 ft. ladder. How far from the base of the house should she set up the ladder so that the top of the ladder is exactly at the bottom of the window?(1 point)
ft.

Answer 1

To determine how far from the base of the house Camila should place the ladder, we can use the Pythagorean theorem. The theorem states that in a right-angled triangle:

\[ a^2 + b^2 = c^2 \]

where:

• \( a \) is the height at which the ladder touches the wall (16 ft),
• \( b \) is the distance from the base of the house to the bottom of the ladder (this is what we want to find), and
• \( c \) is the length of the ladder (20 ft).

We can rearrange the formula to solve for \( b \):

1. Substitute the known values into the equation: \[ 16^2 + b^2 = 20^2 \]

2. Calculate \( 16^2 \) and \( 20^2 \): \[ 256 + b^2 = 400 \]

3. Next, subtract 256 from both sides to isolate \( b^2 \): \[ b^2 = 400 - 256 \] \[ b^2 = 144 \]

4. Now take the square root of both sides to find \( b \): \[ b = \sqrt{144} \] \[ b = 12 \]

Thus, Camila should set up the ladder 12 ft from the base of the house.