Use the Pythagorean Theorem Quick Check

Question

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Question
Sylvia is replacing a piece of siding on her house. To make the 12 ft. ladder stable, the bottom of the ladder needs to be 6 ft. from the base of her house. Applying the Pythagorean Theorem and rounding to the nearest tenth, how high will the ladder reach so that Sylvia can replace the siding?(1 point)
Responses

180 ft.
180 ft.

108 ft.
108 ft.

13.4 ft.
13.4 ft.

10.4 ft.

Answer 1

To find out how high the ladder will reach, we can use the Pythagorean Theorem, which states that in a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The formula is:

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

In this case:

• The length of the ladder (hypotenuse, c) = 12 ft
• The distance from the base of the house (one side, a) = 6 ft
• The height reached by the ladder (the other side, b) = ?

Using the Pythagorean Theorem:

\[ 12^2 = 6^2 + b^2 \]

Calculating the squares:

\[ 144 = 36 + b^2 \]

Now, we can solve for \( b^2 \):

\[ b^2 = 144 - 36 \] \[ b^2 = 108 \]

Now, take the square root of both sides to find \( b \):

\[ b = \sqrt{108} \]

Calculating the square root:

\[ b \approx 10.392 \]

Rounding to the nearest tenth:

\[ b \approx 10.4 \]

So, the height the ladder reaches is approximately 10.4 ft.

The correct response is: 10.4 ft.