Law of Sines and Cosines Calculator
The laws of cosines and sines solve triangles that are not right-angled: b = 8, c = 5 with 60° between them encloses an area of 17.32050808.
17.3205080756888
Full answer, then cut to fewer decimals (not rounded):
- 17.3205080756888
- 17.320508075688
- 17.32050807568
- 17.3205080756
- 17.320508075
- 17.32050807
- 17.3205080
- 17.320508
- 17.32050
- 17.3205
- 17.320
- 17.32
- 17.3
- Side a
- 7
- Side b
- 8
- Side c
- 5
- Angle A
- 60 °
- Angle B
- 81.7867893 °
- Angle C
- 38.2132107 °
- Perimeter
- 20
Step-by-step solution
- Law of cosines: a² = b² + c² − 2bc·cos A
- Law of sines: a/sin A = b/sin B = c/sin C = 8.082903769
- Area = ½·b·c·sin A = 17.32050808
Law of Sines and Cosines Formula
a² = b² + c² − 2bc·cos A; a/sin A = b/sin B = c/sin C
area = ½bc·sin A
Worked Example
A triangle with sides b = 8, c = 5 and angle A = 60° between them:
- Law of cosines: a² = b² + c² − 2bc·cos A
- Law of sines: a/sin A = b/sin B = c/sin C = 8.082903769
- Area = ½·b·c·sin A = 17.32050808
Side b: 8 · Side c: 5 · Angle A: 60 ° · Angle B: 81.7867893 ° · Angle C: 38.2132107 ° · Perimeter: 20
Test-day tip
The ACT allows most graphing calculators; set it to degree mode. For area questions, ½ab·sin C avoids finding the height.
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Frequently asked questions
When do I use the law of cosines instead of the law of sines?
Use cosines for SSS or SAS (no angle opposite a known side); use sines when you know an angle and its opposite side.
Does the ACT give the law of sines?
ACT questions that need it usually quote the formula in the question, but recognising when to apply it is part of the problem.
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Law of Sines and Cosines Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/law-of-sines-cosines-calculator/
IEEE
Scientific Converters, "Law of Sines and Cosines Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/law-of-sines-cosines-calculator/