Working on a Rescue Team LAB Topic Index | Algebra2/Trig Index | Regents Exam Prep Center

This lab utilizes the Law of Sines and the Law of Cosines.

Scenario:  As a rescue team worker, you have been called to Yellowstone National Park to help in rescue efforts to locate a downed private airplane.  Unfortunately, the plane crashed in a densely forested section of the park.  A witness, located 14 miles due east of the Ranger Station, saw the plane go down.  Smoke can be seen rising above the trees.

You and your team are presently 8 miles due west of the location of the witness.

Materials: masking tape, protractor, graphing calculator, string, a large flat surface upon which to work such as a large piece of construction paper, a white board, the chalkboard, etc.

Directions: 
1.  Using string and tape, set up an oblique triangle depicting the situation shown in the diagram above.  The downed airplane is northeast of the location of the witness.  Form the triangle seen in the diagram by taping straight pieces of string to your large flat surface.  Your string should be longer than the actual sides of your triangle so that you can secure the string with tape outside of the triangle. 

2.  Label the Park Ranger Station as S, the location of the witness as W, and the downed plane as P.

3.  Forest Rangers at the station and at the witness location have devices to determine angle readings.  These readings are radioed to your rescue team.  Use your protractor to simulate the taking of these readings.  Determine the number of degrees in angles S and W.  Since you do not know the location of the plane, you cannot physically measure angle P.  How do you determine the size of angle P?

4.  Find the distance from the Ranger Station to the plane.

5.  Find the distance from the location of the witness to the plane.

6.  Label your position as R.  Connect R to P.  Find your direct distance to the plane.

7.  Your rescue team begins a direct trek toward the plane.  After trekking for 4 miles, you are radioed by a helicopter that has arrived on the scene.  The helicopter informs you that an impassable rock cavern is ahead on your current path.  You are informed that you will need to travel one mile due east to avoid the cavern.  After traveling one mile, you resume a direct path to the smoking plane.  Considering the detour, how far did your rescue team travel to get to the plane?