Question

there is a 14 foot ladder leaning up against a wall. the ladder makes a 45 degree angle with the ground. How far above the ground is the ladder touching the wall? leave your answer in radical form. :)

Answer 1

since this is an equilateral triangle (both angles are equal, so both legs are equal) you know that \[a^2+a^2=14^2\] so
\[2a^2=14^2\] or
\[a\sqrt{2}=14\] that makes
\[a=\frac{14}{\sqrt{2}}\]

Answer 2

in general ratios of a 45 - 45 - 90 right triangle are
\[1:1:\sqrt{2}\]

Answer 3

thank you so much:) it was a lot simpler than I thought