Calculate triangle area, perimeter, and angles
Triangles are fundamental geometric shapes with three sides, three angles, and many practical applications. Understanding triangle calculations is essential for construction, engineering, navigation, and many other fields.
When given two sides and a non-included angle (SSA), the triangle may not be uniquely determined. This "ambiguous case" can result in zero, one, or two valid triangles depending on the relationship between the given measurements.
c² = a² + b² - 2ab cos(C)
Used to find a side when two sides and included angle are known
a/sin(A) = b/sin(B) = c/sin(C)
Used to find angles or sides when some combinations are known
c² = a² + b²
Where c is the hypotenuse and a, b are the legs
Area = ½ × base × height
Area = ½ × a × b × sin(C)
Area = √[s(s-a)(s-b)(s-c)] (Heron's Formula)
Where s = (a+b+c)/2 is the semiperimeter
Perimeter = a + b + c
Sum of all three side lengths