Math 120 Notes 8.3 – Law of Cosines
I.
II.
Give the Law of Cosines.
a.
SAS: Find the missing side.
b.
An air traffic controller sights two planes that are due east from the control tower and headed toward
each other. One is 15.8 mi from the tower at an angle of elevation of 26.4º, and the other is 32.7 mi
from the tower at an angle of elevation of 12.4º. How far apart are the planes?
c.
SSS: Find the missing angle.
d.
The distance from Chicago to St. Louis is 440 km, from St. Louis to
Atlanta 795 km, and from Atlanta to Chicago 950 km. What is the
angle determined by St. Louis, Atlanta (vertex), and Chicago?
Combination problem:
A plane flying in a straight line passes directly over point A on the ground and later directly over point B, which
is 3 miles from A. A few minutes after the plane passes over B, the angle of elevation from A to the plane is
43º and the angle of elevation from B to the plane is 67º. How high is the plane at that moment?
What kind What do
What do you
of triangle? you know? want to know?
Use
Right
One angle
SIDE
sin, cos, and tan
One side
Right
Two sides
ANGLE
sin-1, cos-1, and tan-1
Any
AAS
SIDE
Law of Sines
Any
SSA
ANGLE
Law of Sines
Any
SAS
SIDE
Law of Cosines
Any
SSS
ANGLE
Law of Cosines