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 initial distance of the ladder base from the house

We use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 40$ (ladder length - hypotenuse) and $b = 24$ (height on the house). Let the base - distance be $a$. Then $a=\sqrt{c^{2}-b^{2}}=\sqrt{40^{2}-24^{2}}=\sqrt{(40 + 24)(40 - 24)}=\sqrt{64\times16}=\sqrt{1024}=32$ feet.

Step2: Find the new base - distance

The base is pulled 4 feet farther from the house. So the new base - distance $a_{new}=32 + 4=36$ feet.

Step3: Find the new height on the house

Again, using the Pythagorean theorem $a_{new}^{2}+b_{new}^{2}=c^{2}$. We know $a_{new}=36$ and $c = 40$. Then $b_{new}=\sqrt{c^{2}-a_{new}^{2}}=\sqrt{40^{2}-36^{2}}=\sqrt{(40 + 36)(40 - 36)}=\sqrt{76\times4}=\sqrt{304}\approx17.4$ feet.

Answer:

$17.4$ feet