๐ Math
Triangle Calculator
Solve any triangle given 3 known values (angles or sides, with at least one side). Uses the Law of Sines and Law of Cosines to calculate the missing properties.
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Formula
Law of Sines: a/sin(A) = b/sin(B) = c/sin(C) | Law of Cosines: cยฒ = aยฒ + bยฒ - 2abยทcos(C)a, b, c- Side lengths
A, B, C- Opposite angles
Example
Solving a Right Triangle
Find the hypotenuse and remaining angles given two legs a=3, b=4, and angle C=90ยฐ.
- Use Pythagorean theorem for side c: cยฒ = 3ยฒ + 4ยฒ = 9 + 16 = 25.
- Side c = โ25 = 5.
- Find angle A using sin(A) = a/c: sin(A) = 3/5 = 0.6.
- Angle A = arcsin(0.6) โ 36.87ยฐ.
- Find angle B: 180ยฐ - 90ยฐ - 36.87ยฐ = 53.13ยฐ.
Frequently Asked Questions
No. While knowing three angles defines the shape of the triangle, it does not define its size (these are known as similar triangles). You need at least one side length to calculate the exact dimensions.
When you are given two sides and an angle not between them (Side-Side-Angle), there can sometimes be two valid triangles, one valid triangle, or no possible triangle that fits the criteria.