In triangle \(ABC\), \(A=30^\circ\), \(B=70^\circ\), and \(a=8.0\) cm. Find the length of side \(c\).

Find the missing parts of triangle \(ABC\) if \(B=34^\circ\), \(C=82^\circ\), and \(a=5.6\) cm.

A hot-air balloon is flying over a dry lake when the wind stops blowing. The balloon comes to a stop \(450\) feet above the ground at point \(D\) as shown in Figure 9. A jeep following the balloon runs out of gas at point \(A\). The nearest service station is due north of the jeep at point \(B\). The bearing of the balloon from the service station at \(B\) is S \(19^\circ\) E. If the angle of elevation of the balloon from \(A\) is \(12^\circ\), how far will the people in the jeep have to walk to reach the service station at point \(B\)?

Mini Lecture

1. In \(\Delta ABC\), \(A=50^\circ\), \(B=60^\circ\), and \(a=36\) km. Find \(C\) and then find \(c\).

2. In \(\Delta ABC\), \(B=13.4^\circ\), \(C=24.8^\circ\), and \(a=315\) cm. Find all the missing parts.

Find angle \(B\) in triangle \(ABC\) if \(a=2\), \(b=6\), and \(A=30^\circ\).

Find the missing parts in triangle \(ABC\) if \(a=54\) cm, \(b=62\) cm, and \(A=40^\circ\).

Find the missing parts of triangle \(ABC\) if \(C=35.4^\circ\), \(a=205\) ft, and \(c=314\) ft.

Mini Lecture
Solve \(\Delta ABC\) if

1. \(A=30^\circ\), \(b=40\) ft, and \(a=10\) ft.

2. \(A=120^\circ\), \(b=20\) cm, and \(a=30\) cm.

3. \(A=38^\circ\), \(b=41\) ft, and \(a=54\) ft.

Find the missing parts of triangle \(ABC\) if \(A=60^\circ\), \(b=20\) inches, and \(c=30\) inches.

The diagonals of a parallelogram are \(24.2\) cm and \(35.4\) cm, and intersect at an angle of \(65.5^\circ\). Find the length of the shorter side of the parallelogram.

Solve triangle \(ABC\) if \(a=34\) km, \(b=20\) km, and \(c=18\) km.

A plane is flying with an airspeed of \(185\) miles per hour with heading \(120^\circ\). The wind currents are running at a constant \(32\) miles per hour at \(165^\circ\) clockwise from due north. Find the true course and ground speed of the plane.

Mini Lecture

1. Solve \(\Delta ABC\) if \(a=410\) meters, \(c=340\) meters, and \(B=151.5^\circ\)

2. If \(a=38\) meters, \(b=10\) meters, and \(c=31\) meters, find the largest angle.

Find the area of the triangle \(ABC\) if \(A=35.1^\circ\), \(b=2.43\) cm, and \(c=3.57\).

Find the area of triangle \(ABC\) given \(A=24^\circ 10'\), \(B=120^\circ 40'\), and \(a=4.25\) ft.

Find the area of triangle \(ABC\) if \(a=12\) m, \(b=14\) m, and \(c=8.0\) m.

Mini Lecture
Find the area of \(\Delta ABC\) if

1. \(a=41.5\) meters, \(c=34.5\) meters, and \(B=151.5^\circ\).

2. \(A=46^\circ\), \(B=95^\circ\), and \(c=6.8\) meters.

3. \(a=4.8\) yards, \(b=6.3\) yards, and \(c=7.5\) yards.