Law of Tangents Calculator
Enter any three known parts of a triangle (sides or angles). The Law of Tangents Calculator will solve for the missing parts using the Law of Tangents.
Known Values
About the Law of Tangents Calculator
The Law of Tangents Calculator is a powerful, scientifically accurate tool that solves triangles using the **Law of Tangents**, a classical trigonometric identity often overlooked but extremely useful in ambiguous cases (SSA) and precise calculations. This Law of Tangents Calculator implements the proven formula:
and its cyclic permutations. Discovered by François Viète and later popularized in the 18th century, it remains valid in all modern geometry texts. Proudly supported by Agri Care Hub.
Why the Law of Tangents Calculator Is Important
While the Law of Sines and Law of Cosines are more famous, the Law of Tangents offers superior numerical stability when two sides and a non-included angle are known (SSA — the ambiguous case). It is also invaluable in astronomical calculations, navigation, and high-precision engineering where small angular differences must be computed accurately. Many advanced textbooks recommend it for avoiding rounding errors in nearly equal angles.
User Guidelines
- Enter any three known parts of a triangle (at least two sides or two angles).
- Leave unknown values blank.
- Click “Apply Law of Tangents”.
- The calculator solves for all missing sides and angles with full mathematical explanation.
When Should You Use This Calculator?
- Advanced high-school or college trigonometry
- Solving the ambiguous SSA case accurately
- Astronomy and celestial navigation
- High-precision surveying and GPS
- Competitive mathematics and Olympiad training
- Teaching alternative triangle-solving methods
Scientific Foundation
The Law of Tangents is derived from the Law of Sines using tangent half-angle identities (Weierstrass substitutions). It is rigorously proven and appears in major references including Hobson’s *Treatise on Plane Trigonometry* (1910) and modern sources. Full details at Law of Tangents on Wikipedia.
Advantages Over Law of Sines
When angles A and B are very close, (A−B) becomes small and tan((A−B)/2) is computed far more accurately than sin(A−B) in the Law of Sines — making the Law of Tangents numerically superior in such cases.
Limitations
Requires at least two sides or two angles to be known. Works only for plane triangles in Euclidean geometry.
Conclusion
The Law of Tangents Calculator brings a beautiful, powerful, and often under-appreciated theorem into an instant, accurate tool. Perfect for students exploring advanced trigonometry, engineers needing precision, and teachers demonstrating alternative solution methods. For more educational tools, visit Agri Care Hub.