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Section 9.2 Law of Sines- Notes
If none of the angles of a triangle is a right angle, the triangle is called ___________________.
An Oblique triangle can either have three acute angles or one obtuse angle and two acute angles.
Today, we will discuss how to solve oblique triangles.
To solve an oblique triangle means to find ____________________AND
_________________________.
BUT how to solve the oblique triangle will depend on the information you have. There are 4 cases:
 Cases 1 and 2 can be solved using the LAW OF SINES.
 Cases 3 and 4 require the LAW OF COSINES (NEXT CLASS).
Law of Sines:
a
b
c


sin A sin B sin C
Note: The information provided determines how many possible triangles you may have.
 If you are given two angles, you will only have one triangle.
Example 1 (SAA): Solve the triangle with A = 640, C = 820, and c = 14 centimeters. Round sides to
tenths place.
Example 2 (ASA): Solve the triangle if A = 400, C = 22.50, and b = 12 inches. Round sides to tenths
place.
 The Ambiguous Case: If you are given SSA, you may have No Triangle, One Triangle, or Two
Triangles.
When solving the SSA Case:
You must check to see if the supplement of the first angle could also create a triangle.
IF IT IS, YOU HAVE TWO TRIANGLES!
Example 3 (Two Triangles). Solve the triangle if A = 350, a = 12, b = 16.
Example 4 (One Triangle). Solve the triangle if A = 570, a = 33 meters, and b = 26 meters.
You will have no triangle if when you solve for the 1st angle in the problem you get an error.
Remember that sine is only defined between: −1 to 1.
Example 5 (No Triangle) Solve the triangle if A = 500, a = 10 feet, and b = 20 feet.