Question

a 50 foot ladder is set against the side of a house so that it reaches up 48 feet. if mila grabs the ladder at its base and pulls it 6 feet farther from the house, how far up the side of the house will the ladder reach now? (the answer is not 42 ft.) round to the nearest tenth of a foot.

Explanation:

Step1: Find initial distance from house base

We use the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 50$ (ladder length) and $b = 48$ (height on house). Let the initial distance from the base of the house to the base of the ladder be $a$. So $a=\sqrt{c^{2}-b^{2}}=\sqrt{50^{2}-48^{2}}=\sqrt{(50 + 48)(50 - 48)}=\sqrt{98\times2}=\sqrt{196}=14$ feet.

Step2: Calculate new distance from house base

The base of the ladder is pulled 6 feet farther from the house. So the new distance from the base of the house to the base of the ladder is $a_{new}=14 + 6=20$ feet.

Step3: Find new height on house

Again, using the Pythagorean theorem with $c = 50$ and $a_{new}=20$. Let the new height on the house be $b_{new}$. Then $b_{new}=\sqrt{c^{2}-a_{new}^{2}}=\sqrt{50^{2}-20^{2}}=\sqrt{(50 + 20)(50 - 20)}=\sqrt{70\times30}=\sqrt{2100}\approx45.8$ feet.

Answer:

$45.8$ feet