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Law of Sines:
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The Law of Sines is a trigonometric equation relating the lengths of sides of a triangle to the sines of its opposite angles. It states that the ratio of the length of a side to the sine of its opposite angle is constant for all three sides and angles in a triangle.
The calculator uses the Law of Sines:
Where:
Explanation: The calculator requires at least three elements (including at least one side) to solve the triangle completely. It first calculates missing angles using the angle sum property (A + B + C = 180°), then uses the Law of Sines to find missing sides.
Details: Solving triangles is fundamental in geometry, navigation, engineering, and physics. The Law of Sines is particularly useful for solving oblique triangles (non-right triangles).
Tips: Enter any three known elements (including at least one side). The calculator will determine the remaining elements. All angles must be in degrees, and sides must be positive values.
Q1: What's the minimum information needed to solve a triangle?
A: You need at least three elements, including at least one side length. Possible combinations: two angles and one side, two sides and one angle, or three sides.
Q2: Why does the calculator require at least one side?
A: Without at least one side length, the triangle can be solved for shape but not for size (you'd get proportions but not actual lengths).
Q3: What if my angles don't add up to 180°?
A: The calculator will adjust the third angle to make the sum exactly 180°. If two given angles already sum to 180° or more, the triangle is impossible.
Q4: Can this solve right triangles?
A: Yes, though right triangles can also be solved using the Pythagorean theorem and basic trigonometric ratios.
Q5: What about the ambiguous case (SSA)?
A: When given two sides and a non-included angle (SSA), there may be two solutions. This calculator will return one valid solution.