Question

a 40 foot ladder is set against the side of a house so that it reaches up 24 feet. if lily grabs the ladder at its base and pulls it 4 feet farther from the house, how far up the side of the house will the ladder reach now? (the answer is not 20 ft.) round to the nearest tenth of a foot.

Explanation:

Step1: Find the original distance of the ladder base from the house

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(c = 40\) (ladder length) and \(b = 24\) (height on the house). Let \(a\) be the base - distance.

$$a=\sqrt{c^{2}-b^{2}}=\sqrt{40^{2}-24^{2}}=\sqrt{(40 + 24)(40 - 24)}=\sqrt{64\times16}=\sqrt{1024}=32$$

Step2: Find the new base - distance

The new base - distance \(a_{new}=32 + 4=36\)

Step3: Find the new height on the house

Again, use the Pythagorean theorem \(a_{new}^{2}+b_{new}^{2}=c^{2}\), where \(c = 40\) and \(a_{new}=36\). Solve for \(b_{new}\)

$$b_{new}=\sqrt{c^{2}-a_{new}^{2}}=\sqrt{40^{2}-36^{2}}=\sqrt{(40 + 36)(40 - 36)}=\sqrt{76\times4}=\sqrt{304}\approx17.4$$

Answer:

\(17.4\) feet