Question

1. find ps.

Explanation:

Step1: Find length of QS

In right $\triangle QRS$, use $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$
$\tan(28^\circ)=\frac{QS}{39}$
$QS = 39\times\tan(28^\circ) \approx 39\times0.5317 = 20.7363$

Step2: Find length of PS

In right $\triangle PQS$, use $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$
$\cos(76^\circ)=\frac{PQ}{PS}$, and $\sin(76^\circ)=\frac{QS}{PS}$
$PS=\frac{QS}{\sin(76^\circ)}$
$PS \approx \frac{20.7363}{0.9703} \approx 21.37$

Answer:

$\approx 21.4$ (rounded to one decimal place, or exact form $PS=\frac{39\tan(28^\circ)}{\sin(76^\circ)}$)