Triangle Area from One Side and Two Angles (ASA)

Find the area, the remaining two sides, and the third angle of a triangle from one side and its two adjacent angles (ASA) using the law of sines.

Input

Enter the length of one side and the two angles A and B at its ends to find the area of the triangle.

Angle unit

Side c (the side between angles A and B)

Angle A

deg

Angle B

deg

Triangle area

35.299519

Side c

Side a (opposite A)

8.152075

Side b (opposite B)

9.21605

Angle C (third angle)

70 deg

Perimeter

27.368125

Lengths use the same unit as the side you entered, and the area uses that unit squared.

The third angle is found from C = 180 − A − B in degrees. The triangle exists only when A plus B is less than 180 degrees.
The remaining sides come from the law of sines a / sinA = b / sinB = c / sinC, where a is opposite angle A and b is opposite angle B.
The area is computed as S = (1/2) × a × b × sinC.
Lengths share the unit of the side you entered, and the area uses that unit squared.
Angles can be entered in degrees or radians.

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