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
- Angles
- A = 33.55730976°, B = 50.70351976°, C = 95.73917048°
- Area
- 17.41228015
- Perimeter
- 21
Solution
| # | a | b | c | A | B | C | Area |
|---|---|---|---|---|---|---|---|
| 1 | 5 | 7 | 9 | 33.55730976° | 50.70351976° | 95.73917048° | 17.41228015 |
Show the work
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
How it works
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°
Questions
- 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.
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