Question

The base of a ladder 22 feet long is placed on the ground 6 feet from the side of a house. Which of the following is closest to how high up on the top of the ladder reaches

A) 22.8 feet

B) 21.2 feet

C) 19.5 feet

D) 16.0 feet

Answer 1

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}{22}\\ a=\stackrel{adjacent}{6}\\ o=\stackrel{opposite}{h} \end{cases} \\\\\\ h=√( 22^2 - 6^2)\implies h=√( 484 - 36 ) \implies h=√( 448 )\implies h\approx 21.2`