Question

Express cos S as a fraction in simplest terms.

Answer 1

let's first off find the hypotenuse QS

`\begin{array}{llll} \textit{using the pythagorean theorem} \\\\ c^2=a^2+o^2 \end{array} \qquad \begin{cases} c=\stackrel{hypotenuse}{QS}\\ a=\stackrel{adjacent}{√(59)}\\ o=\stackrel{opposite}{√(62)} \end{cases} \\\\\\ (QS)^2= (√(59))^2 + (√(62))^2\implies QS^2=59+62 \\\\\\ QS^2=121\implies QS=√(121)\implies QS=11~\hfill~\boxed{\cos(S )=\cfrac{\stackrel{adjacent}{√(59)}}{\underset{hypotenuse}{11}} }`

Check the picture below.