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Algebra II/Trigonometry Honors
Unit 9 Day 3: Solving Oblique Triangles
Objective: To use the Law of Cosines and the Law of Sines to solve for missing sides and angles in non-right
triangles
To solve for missing sides or angles in right triangles, you used _______________________
To solve for missing sides or angles in non-right triangles, we will use ___________________
Law of Sines (You must have an angle-side pair to use Law of Sines!!)
sin A sin B sin C


a
b
c
The Law of Sines can be used when you have:
 ASA (you know two angles and the length
of the side between the angles)

AAS (you know two angles and the length
of the side NOT between the angles)

SSA (you know the length of two sides and
an angle NOT between the sides)
Example 1: Solve a triangle for the AAS case
Solve ABC with C  107 , B  25 , and b  15
Solve ABC with B  34 , C  100 , and b  8
Example 2: Solve a triangle for the ASA case
Solve ABC for A  51 , B  44 , c  11
Solve ABC with A  94 , C  67 , and b  25
Law of Cosines (can be used when you have):
 SAS (you know two sides, and you know the angle between the two sides)
 SSS (you know all three sides…find largest angle first!!!)
If ABC has sides of length a, b, and c as shown, then:
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



You MUST find largest angle first!
 A is across from side a,  B is across from
side b, and C is across from side c.
Lowercase letters are sides. Uppercase letters
are angles.
Example 1: Solve a triangle for the SAS case
Solve ABC with a  11 , c  14 , and B  34
Example 2: Solve a triangle for the SSS case
Solve ABC with a  12 , b  27 , and c  20 .
An airplane flies N 55 E from City A to City B a distance of 470 miles. From City B, the plane flies N 20 W to
City C City C and then returns back to City A.. Determine how far the plane must travel from City B to reach
City A. City A is directly below City C.
Scientists can use a set of footprints to calculate an organism’s step angle, which is a measure of walking
efficiency. The closer the step angle is to 180 , the more efficiently the organism walked. The diagram at the
right shows a set of footprints for a dinosaur. Find the step angle B.
HW: Worksheet