College Algebra & Trigonometry, 2018a

11.4. APPLICATIONS 507
4. An airplane leaves airport A and travels 520 miles to airport B at a bearing
of N35 ◦ W . The plane leaves airport B and travels to airport C 310 miles away at
a bearing of S65 ◦ W from airport B. Find the distance from airport A to airport C.
5. Two planes take off at the same time from an airport. The first plane flies at
300 mph at a bearing of S45 ◦ E. The second plane is flying at a bearing of S5 ◦ W
with a speed of 330 mph. How far apart are they after 3 hours?
6. Two planes leave an airport at the same time. Their speeds are 180 mph
and 110 mph, and the angle between their flight paths is 43 ◦ . How far apart are
they after 2.5 hours?
7. Two ships leave a harbor entrance at the same time. The first travels at
a speed of 23 mph and the second travels at 17 mph. If the angle between the
courses of the ships is 110 ◦ , how far apart are they after one hour?
8. A ship leaves the entrance to a harbor and travels 15 miles with a bearing
S10 ◦ W , then turns and travels 45 miles with a bearing of N43 ◦ W . How far
from the harbor entrance is the ship and what is the bearing of the ship from the
harbor?
9. A steep mountain is inclined 77 ◦ to the horizontal and rises 3000 feet above
the surrounding plain. A cable car is to be installed that will connect the plain
to the top of the mountain. The distance from the foot of the mountain to the
cable car entry loading area is 1200 feet (see diagram below). Find the shortest
necessary length of the cable.
3000 ft
1200 feet
cable car loading area
77 ◦