Question

A 50 foot ladder is set against the side of a house so that it reaches up 48 feet. If Jack 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 44 ft.) Round to the nearest tenth of a foot

Answer 1

Check the picture below.

before Jack moved the ladder

`\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies √(c^2 - b^2)=a \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ √(50^2 - 48^2)=x\implies √(196)=x\implies \boxed{14=x}`

after Jack pulled the ladder

`\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies √(c^2 - a^2)=b \qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ √(50^2 - (x+4)^2)=y\implies √(50^2 - (14+4)^2)=y \\\\\\ √(50^2 - 18^2)=y\implies √(2176)=y\implies \boxed{46.6\approx y}`