Question

Find cosec(b). see attached photo for diagram.

Answer 1

Check the picture below.

let's find the hypotenuse AB

`\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}{AB}\\ a=\stackrel{adjacent}{10}\\ o=\stackrel{opposite}{6} \end{cases} \\\\\\ AB=√( 10^2 + 6^2)\implies AB=√( 100 + 36 ) \implies AB=√( 136 ) \\\\[-0.35em] ~\dotfill\\\\ \csc(B )=\cfrac{\stackrel{hypotenuse}{√(136)}}{\underset{opposite}{6}}\implies \csc(B )=\cfrac{2√(34)}{6}\implies \csc(B )=\cfrac{√(34)}{3}`