Question

Find the value of sec θ for the angle shown

Answer 1

$\bf (\stackrel{\stackrel{x}{adjacent}}{7}~~,~~\stackrel{\stackrel{y}{opposite}}{6})\impliedby \textit{let's find the \underline{hypotenuse}} \\\\\\ \textit{using the pythagorean theorem}\\\\ c^2=a^2+b^2\implies c=\sqrt{a^2+b^2}\qquad \begin{cases} c=hypotenuse\\ a=adjacent\\ b=opposite\\ \end{cases} \\\\\\ c=\sqrt{7^2+6^2}\implies c=\sqrt{85}\\\\ -------------------------------\\\\ sec(\theta)=\cfrac{hypotenuse}{adjacent}\qquad \qquad sec(\theta)=\cfrac{\sqrt{85}}{7}$