Question

use the pythagorean theorem quick check
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)
10.8 ft
18.0 ft
10.4 ft
13.4 ft

Explanation:

Step1: Identify the Pythagorean Theorem formula

The Pythagorean Theorem is \(a^{2}+b^{2}=c^{2}\), where \(c\) is the hypotenuse (length of the ladder, \(c = 12\) ft) and \(a\) is the base (distance from the house, \(a=6\) ft). We need to find \(b\) (height on the house).

Step2: Rearrange the formula to solve for \(b\)

$$b=\sqrt{c^{2}-a^{2}}$$

Substitute \(c = 12\) and \(a = 6\) into the formula:

$$b=\sqrt{12^{2}-6^{2}}=\sqrt{144 - 36}=\sqrt{108}$$

Step3: Calculate the value of \(\sqrt{108}\)

\(\sqrt{108}\approx10.4\) (rounded to the nearest tenth)

Answer:

10.4 ft