Download In certain navigation or surveying problems, the direction or bearing

MA 154
Section 6.7
Lesson 11
Applied Problems
Delworth
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.
N
A
D
30

35

70

W
C
P
75

E
B
S
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.
1
MA 154
Section 6.7
Lesson 11
Applied Problems
Delworth
A ship leaves port and sails in the direction N78W at a rate of 35 mph. At the same time,
another ship leaves the same port in the direction S12W 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?
2
MA 154
Section 6.7
Lesson 11
Applied Problems
Delworth
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.
N
A
30
.
P
B
45
3
MA 154
Section 6.7
Lesson 11
Applied Problems
Delworth
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?
4