Question

Given RP = 22, RA = 6, and PQ is tangent to .R at Q, find PQ.

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}{PQ} \end{cases} \\\\\\ PQ=√( 22^2 - 6^2)\implies PQ=√( 484 - 36 ) \implies PQ=√( 448 )\implies PQ\approx 21.17`