Question

A 30 foot ladder is set against the side of a house so that it reaches up 24 feet. If Alexander grabs the ladder at its base and pulls it 10 feet farther from the house, how far up the side of the house will the ladder reach now? (The answer is not 14 ft.) Round to the nearest tenth of a foot. Solve using the Pythagorean theorem

Answer 1

well, first off, what was the bottom distance in that triangle with hypotenuse of 30 and hmmm a side of 24?

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies a=√(c^2 - o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{bottom}\\ o=\stackrel{opposite}{24} \end{cases} \\\\\\ bottom=√( 30^2 - 24^2) \implies bottom=√( 324 )\implies bottom=18`

Check the picture below.

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ a^2+o^2=c^2\implies o=√(c^2 - a^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{30}\\ a=\stackrel{adjacent}{28}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=√( 30^2 - 28^2)\implies h=√( 900 - 784 ) \implies h=√( 116 )\implies h\approx 10.8`