Question

How do I solve using theorem of pythagoras​

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}{14}\\ a=\stackrel{adjacent}{8}\\ o=\stackrel{opposite}{z} \end{cases} \\\\\\ z=√( 14^2 - 8^2)\implies z=√( 196 - 64 ) \implies z=√( 132 ) \\\\[-0.35em] ~\dotfill`

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2\implies c=√(a^2 + o^2) \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{p}\\ a=\stackrel{adjacent}{21}\\ o=\stackrel{opposite}{√(132)} \end{cases} \\\\\\ p=\sqrt{ 21^2 + (√(132))^2}\implies p=√( 441 + 132 ) \implies p=√( 573 )\implies p\approx 23.9`