Download Law of Sines and Cosines

Law of Sines and Cosines
Analysis
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1. An airplane A takes off from carrier B and flies in a straight
line for 12 miles. At that instant, an observer on destroyer C
located 5 miles from the carrier, notes that the angle
determined by the carrier, the destroyer (vertex) and the
plane is 37°. How far is the plane from the destroyer?
2. A 100-foot-tall antenna tower is to be placed on a hillside that
makes an angle of 12° with the horizontal. It is to be anchored
by tow cables from the top of the tower to points 85 feet
uphill and 95 feet downhill from the base. How much cable is
needed?
3. A plane flying in a straight line passes directly over a point A
on the ground and later over a point B which is 3 miles from A.
A few minutes later after the plane passes over B. the angle of
elevation from A to the plane is 43° and the angle of elevation
from B to the plane is 67°. How high is the plane at that
moment?
4. Two trains leave a station on different tracks. The tracks
make an angle of 125° with the station as vertex. The first
train travels at an average speed of 100 miles per hour and the
second travels at an average speed of 65 miles per hour. How
for apart are the two trains after 2 hours?
5. A forest fire is spotted from two fire towers. The triangle
determined by the two towers and the fire has angles of 28°
and 37° at the tower vertices. If the towers are 3000 meters
apart, which one is closer to the fire?
Law of Sines/Cosines
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Analysis
6. At Wrigley Field in Chicago, the straight-line distance from
home plate over second base to the centerfield wall is 400
feet. How far is it from first base to the same point at the
centerfield wall?
7. If a gallon of paint covers 400 square feet, how many gallons
are needed to paint a triangular deck with sides of 65 feet, 72
feet, and 88 feet?
8. A boat runs in a straight line for 3 miles, and then it makes a
45° turn and goes for another 6 miles. How far is the boat
from its starting point?
9. One diagonal of a parallelogram is 6 inches long and the other
is 13 inches long. They form a 42° angle with each other. How
long are the sides of a parallelogram? (Hint: the diagonals of
a parallelogram bisect each other.)
10.
Find the angles of a triangle whose vertices are (0,0), (5,-2),
and (1,-3).
Law of Sines/Cosines
Analysis
B
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7.35 "
C
20.62"
A
8.04"
11. Assuming that the circles in the figure are mutually tangent,
find the lengths of sides and the measures of the angles of
triangle ABC.