Question

How do I solve this???

Answer 1

`\mathrm{Take\ the\ known\ angle\ except\ for\ the\ right\ angle.\ Taking\ 67^o\ as\ reference,\ it's}\\\mathrm{opposite\ side\ has\ length\ equal\ to\ 16.\ This\ side\ (16)\ opposite\ to\ the\ angle}\\\mathrm{taken\ in\ reference\ (i.e.\ 67^o)\ is\ perpendicular(p).}\\\mathrm{So,\ we\ are\ asked\ to\ find\ hypotenuse(h)\ while\ we\ are\ given\ reference\ angle\ \theta}\\\mathrm{and\ perpendicular\ length\ p.}\\\mathrm{Now\ we\ can\ use\ either\ sine\ or\ cosecant\ to\ find\ the\ answer.}\\`

`\mathrm{We\ have}\\\mathrm{sin}\theta=\mathrm{(perpendicular)/(hypontenuse)}\\\\\mathrm{or,\ sin67^o}=(16)/(x)\\\mathrm{or,\ }x=\frac{16}{\mathrm{sin}67^o}\\\\\mathrm{or,\ }x=17.38`

If you are using cosecant to find 'x', use hypotenuse/perpendicular.