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Law of Sines
The Law of Sines
The Law of Sines can be used to solve triangles that
are not right.
Let ABC by any triangle with a, b, and c
representing the measures of the sides opposite the
agles with the measures A, B, and C respectively.
Then, the following is true:
Law of Sines
Proof:
Think back to geometry:
Unique triangles can be formed if you know the
measures of certain angles and sides.
When you know the measure of two angles and the included
side (ASA), two sides and the included angle, or the
measures of two angles and the non-included side (AAS),
there is one unique triangle that is formed.
Therefore, there is one unique solution when you use the
Law of Sines given those certain parts.
Law of Sines
ASA
47. 3
12.4
33
AAS
105
33
37.9
Law of Sines
Solve triangle LMN if L=29, M=112, and l=22.
Try these:
Solve each triangle. Round to the nearest tenth.
1. A=40, C=70, a=20.
2. b=12, A=25, B=35.
3. B=100, C=50, c=30
4. a=8.2, B=24.8, C=61.3
Law of Sines
Finding the area of any triangle:
Let K represent the area of the triangle (we aren't using A
since it represents the angle measures of our triangle)
Example:
Find the area of DEF if d=13.9, D=34.4 and E=14.8.
Law of Sines
Try These:
Find the area of each triangle. Round to the nearest tenth.
1. A=28, b=14, c=9
2. a=5, B=37, C=84
3. B=42.8, a=12.7, c=5.8
4. a=19.2, A=53.8, C=65.4
In order to avoid a storm, a pilot starts the flight 13 degrees off
course. After flying 80 miles in this direction, the pilot turns the
plane to head toward the destination. The angle formed by the
course of the plane during the first part of the flight and the course
during the second part of the flight is 160 degrees. What is the
length of the direct course from airport to airport?
Law of Sines