6.1: Law of Sines

6.1: LAW OF SINES

To solve an oblique triangle you MUST have any of the four cases to be solved with law of sines:

• Two angles and any side (ASA)
• Two sides and an angle opposite one of them (SSA)

The Ambiguous Case

When given two sides and an angle, you have an ambiguous case. There are three situations of triangles.

1. Single Solution Case

• The above triangle is a single solution triangle
• You can solve for this triangle using the Law of Sines
• ONE SOLUTION because angle A is acute, and a > b

       2. No Solution Case

• In the above triangle, angle A is on the left, angle C is on top, and angle B is on the right
• No triangle can be formed from these dimensions given
• If you were to drop an altitude, you would find that a < h, which is impossible

       3. Two Solutions Case

• In the above triangle, angle A is on the left, angle C is on top, and angle B is on the right
• In this case, with the given dimensions, two triangles can be made
• This is because (h < a < b)
• When you solve for angle B, you must solve for both angles that answer sinB
• subtract the answer you get from 180
• you will have made two triangles that must be solved, as seen in the right two triangles

Area of an Oblique Triangle 

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