Solve the remaining sides and angle from one opposite pair and another angle. The page traces how the inputs become solved asa/aas triangle before rounding.
ASA and AAS triangles are solved directly once one side-angle opposite pair is known.
The law of sines states that each side divided by the sine of its opposite angle has the same circumdiameter ratio. Law of Sines can be compared with SSA branch test.
The Law of Sines case starts with Known angle A in degrees and Opposite side a. Recalculate Solved ASA/AAS triangle from those entries. A nearby Second angle B in degrees can challenge the Law of Sines relationship, but its Solved ASA/AAS triangle belongs to a separate Law of Sines record.
Angle labels must stay paired with their opposite sides. The three angles must sum to 180°.
A=40°, a=8, and B=65° determine C=75° and both remaining sides.
Find the third angle, set two sine proportions, and verify that the longest side faces the largest angle.
Start the Law of Sines review with Known angle A in degrees. Compare Known angle A in degrees with its source, then test Opposite side a in a second Law of Sines run without changing the first Law of Sines case.
Link Known angle A in degrees to its Law of Sines role. Link Opposite side a to its Law of Sines role. The retained Law of Sines formula identifies the Law of Sines model.
Law of Sines uses Known angle A in degrees, Opposite side a, and Second angle B in degrees. Substitute the result into the forward relationship when possible. Inverse and triangle calculations are easier to verify by reconstructing the supplied ratio or side condition.
For this law of sines result, record the known-data pattern—such as SAS, ASA, or SSA—alongside the solved triangle.
Choose a familiar Known angle A in degrees and rerun Law of Sines. With Opposite side a unchanged, estimate Solved ASA/AAS triangle by hand. This small Law of Sines case provides context for the original Solved ASA/AAS triangle without duplicating it.
The law of sines states that each side divided by the sine of its opposite angle has the same circumdiameter ratio.
ASA and AAS triangles are solved directly once one side-angle opposite pair is known.
Angle labels must stay paired with their opposite sides. The three angles must sum to 180°.