MA 154Lesson 11Delworth
Section 6.7Applied Problems
In certain navigation or surveying problems, the direction or bearing, from a point P to a point Q is specified by stating the acute angle that segment PQ makes with the north-south line through P. We also state whether Q is north or south and east or west of P.
Notice that when this notation is used for bearings or directions, N or S always appears to the left of the angle and W or E to the right.
Before we go into the application problems for this set, remember back to your days in Geometry? Remember when two parallel lines are cut by a transversal?
and are supplementary since they are the two angles that determine a line.
= and = since they are alternate interior angles
and are supplementary since they are same-side interior angles.
A ship leaves port and sails in the direction N78W at a rate of 35 mph. At the same time, another ship leaves the same port in the direction S12W at a rate of 21 mph.
a)How far apart are the two ships after 3 hours?
b)What is the bearing, to the nearest degree, from the first ship to the second?
In air navigation, directions and bearings are specified by measuring from the north in a clockwise direction. In this case, a positive measure is assigned to the angle instead of the negative measure to which we are accustomed for clockwise rotations.
An Airplane, flying at 300 miles per hour, flies in the direction 100 for 2 hours. It then flies in the direction 190 for 1.5 hours
a)Find the distance from the start point to the plane after the 3.5 hour flight.
b)In what direction does the plane need to fly to get back to its start point?
c)How long will it take for the plane to reach its start point?
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