To find the values of side PS we can use the trignometric functions to find the different measures of the 2 right triangles on the image.
First start by finding the measure of side QS using the triangle on the right ant the angle of 28°.
The trigonometric function taht involves the side given QR and the missing side QS is the tan.
[tex]\begin{gathered} \tan (28)=\frac{QS}{QR} \\ QS=QR\cdot\tan 28 \\ QS=39\cdot\tan (28) \end{gathered}[/tex]
after having the value of QS express side PS using the sin of 76°
[tex]\begin{gathered} \sin 76=\frac{QS}{PS} \\ PS=\frac{QS}{\sin 76} \\ PS=\frac{39\cdot\tan (28)}{\sin (76)} \\ PS\approx21.4 \end{gathered}[/tex]
