Question

1. find ps.

Explanation:

Step1: Find \(QS\)

In right - triangle \(QSR\), \(\sin R=\frac{QS}{SR}\). Given \(R = 28^{\circ}\) and \(SR = 39\).
\(\sin28^{\circ}=\frac{QS}{39}\), so \(QS = 39\times\sin28^{\circ}\approx39\times0.4695 = 18.3105\).

Step2: Find \(PS\)

In right - triangle \(PQS\), \(\sin P=\frac{QS}{PS}\). Given \(P = 76^{\circ}\) and \(QS\approx18.3105\).
\(\sin76^{\circ}=\frac{18.3105}{PS}\), then \(PS=\frac{18.3105}{\sin76^{\circ}}\). Since \(\sin76^{\circ}\approx0.9703\), \(PS=\frac{18.3105}{0.9703}\approx18.9\).

Answer:

\(PS\approx18.9\)