Download Algebra II/Trigonometry - Garnet Valley School District

Geometry A Unit 9 Day 6 Notes
The Law of Sines
Objective:
 To use the law of sines to find the sides and angles of triangles (round all answers to the
nearest tenth unless otherwise noted)
When to use…
SOH CAH TOA ______________________________________________________
sin  
length of side opposite 
length of hypotenuse
cos  
length of side adjacent 
length of hypotenuse
tan  
length of side opposite 
length of side adjacent 

Adjacent
Law of Cosines________________________________________________________
In any triangle,
A
c
b
B
a
a 2  b 2  c 2  2bc cos A
b 2  a 2  c 2  2ac cos B
c 2  a 2  b 2  2ab cos C
C
Law of Sines__________________________________________________________
In any triangle,
A
c
sin A sin B sin C


a
b
c
b
B
C
a
We can summarize the times that we use the Law of Sines “you know a matching set of side
and angle” in a non-right triangle.
AAS – given two angles and a side.
In ABC , B  64, a  15, A  38. Solve for side b.
ASA – given two angles and an included side.
ABC , a  8, B  64, C  38. Solve the triangle.
Examples:
1. How long is the base of an isosceles triangle if each leg is 27 cm and each base angle
measures 23 degrees?
2. Two angles of a triangle measure 32 degrees and 53 degrees. The longest side is 55 cm.
Find the length of the shortest side.
3. A fire is sighted from two ranger stations that are 5000 m apart. The angles of
observation to the fire measure 52 degrees from one station and 41 degrees from the other
station. Find the distance along the line of sight to the fire from the closer of the two
stations.
52o
41o
4. Two markers are located at points A and B on opposite sides of a lake. To find the
distance between the markers, a surveyor laid off a base line, AC , 25 m long and found
that BAC  85 and BCA  66. Find AB.
A
C
B
5. The captain of a freighter 6 km from the nearer of two unloading docks on the shore finds
that the angle between the lines of sight to the two docks is 35 degrees. If the docks are
10 km apart, how far is the tanker from the farther dock?
HW: Handout