What do I need to enter?

I know, Side a, Side b, Side c, Angle A (opposite a), Angle B (opposite b), Angle C (between a and b), Units. Optional fields can be left blank.

Triangle Solver

Solve any triangle from three known parts — SSS, SAS, ASA, AAS or SSA (showing both triangles in the ambiguous case).

Triangle

a = 5, b = 7, c = 9

Solution

#	a	b	c	A	B	C	Area
1	5	7	9	33.55730976°	50.70351976°	95.73917048°	17.41228015

Angle A from the law of cosines
A = arccos((p^{to the power of 2} + q^{to the power of 2} − a^{to the power of 2}) ÷ 2pq), with p and q the other two sides
arccos((7^{to the power of 2} + 9^{to the power of 2} − 5^{to the power of 2}) ÷ (2 × 7 × 9)) = 33.55730976°
Angle B from the law of cosines
B = arccos((p^{to the power of 2} + q^{to the power of 2} − b^{to the power of 2}) ÷ 2pq), with p and q the other two sides
arccos((5^{to the power of 2} + 9^{to the power of 2} − 7^{to the power of 2}) ÷ (2 × 5 × 9)) = 50.70351976°
Angle C: the angles add to 180°
C = 180° − A − B
180° − 33.55730976° − 50.70351976° = 95.73917048°
Solved triangle: the three sides
check: A + B + C = 33.55730976° + 50.70351976° + 95.73917048° = 180°
a = 5, b = 7, c = 9

Law of cosines c² = a² + b² − 2ab cos C for SSS/SAS; law of sines a ÷ sin A = b ÷ sin B = c ÷ sin C otherwise; angles add to 180°

How does the triangle solver work?: Law of cosines c² = a² + b² − 2ab cos C for SSS/SAS; law of sines a ÷ sin A = b ÷ sin B = c ÷ sin C otherwise; angles add to 180°.
What do I need to enter?: I know, Side a, Side b, Side c, Angle A (opposite a), Angle B (opposite b), Angle C (between a and b), Units. Optional fields can be left blank.