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Triangles

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1
The Law of Sines

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 \(B\)?