Question

a 35 foot ladder is set against the side of a house so that it reaches up 28 feet. if bentley 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 24 ft.) round to the nearest tenth of a foot.

Explanation:

Step1: Find initial distance from house

Use Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 35$ (ladder length) and $b = 28$ (height on house). Let $a$ be distance from house. So $a=\sqrt{c^{2}-b^{2}}=\sqrt{35^{2}-28^{2}}=\sqrt{(35 + 28)(35 - 28)}=\sqrt{63\times7}=\sqrt{441}=21$ feet.

Step2: Calculate new distance from house

The new distance from the house is $21 + 4=25$ feet.

Step3: Find new height on house

Again use Pythagorean theorem. Let new height be $h$. Then $h=\sqrt{35^{2}-25^{2}}=\sqrt{(35 + 25)(35 - 25)}=\sqrt{60\times10}=\sqrt{600}\approx24.5$ feet.

Answer:

$24.5$ feet