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.