Як розрахувати Triangle Solver
Що таке Triangle Solver?
A triangle solver computes all unknown sides and angles of a triangle from the known values. It handles SSS (three sides), AAS/ASA (two angles and one side), and SAS cases.
Формула
SSS: law of cosines cos(C) = (a²+b²−c²)/(2ab); AAS/ASA: law of sines a/sin(A) = b/sin(B) = c/sin(C)
- a, b, c
- side lengths (length)
- A, B, C
- angles opposite to sides a, b, c (degrees)
Покрокова інструкція
- 1SSS: use the law of cosines to find angles
- 2AAS/ASA: use the law of sines after finding the third angle
- 3Third angle = 180° − (sum of other two)
- 4Area via Heron's formula once all sides are known
Розв'язані приклади
Введення
Sides 3, 4, 5
Результат
Angles: 36.87°, 53.13°, 90° — right triangle, Area = 6
Введення
Angles 30°, 60°, side 10
Результат
Remaining sides computed via law of sines
Часті запитання
What are the four triangle solving cases?
SSS (three sides), SAS (side-angle-side), AAS (angle-angle-side), and ASA (angle-side-angle).
Can AAA (three angles) determine a unique triangle?
No, AAA only gives shape but not size. Infinitely many similar triangles share the same angles.
What is the ambiguous case in triangle solving?
SSA (side-side-angle) can have 0, 1, or 2 solutions depending on the values—it's ambiguous and requires careful analysis.
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