Question

1. solve for side w. 28 cm w 52° 79°

Explanation:

Step1: Find the third angle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(A\).
\(A = 180^{\circ}-(52^{\circ}+79^{\circ})=180^{\circ}-131^{\circ} = 49^{\circ}\)

Step2: Apply the Law of Sines

The Law of Sines states \(\frac{a}{\sin A}=\frac{b}{\sin B}\). Here, if \(a = 28\) (opposite \(49^{\circ}\)) and \(b = w\) (opposite \(79^{\circ}\))
\(\frac{28}{\sin49^{\circ}}=\frac{w}{\sin79^{\circ}}\)
\(w=\frac{28\times\sin79^{\circ}}{\sin49^{\circ}}\)
We know that \(\sin49^{\circ}\approx0.7547\) and \(\sin79^{\circ}\approx0.9816\)
\(w=\frac{28\times0.9816}{0.7547}\)
\(w=\frac{27.4848}{0.7547}\approx36.4\)

Answer:

\(w\approx36.4\space cm\)