SSS Triangle Calculator

FAQs

How do I solve SSS triangles?

SSS means we know all three sides of a triangle. To solve an SSS triangle: Apply the law of cosines to sides a and b to determine the angle between these sides: γ = acos((a² + b² − c²)/(2ab)) Apply again the law of cosines to a and c to determine the angle β. Compute the remaining angle as α = 180° - β - γ . If you wish to determine the area, compute Area = ½ ab sin γ or use the Heron formula: Area=√(s(s - a)(s - b)(s - c)), where s = (a + b + c)/2.

Are SSS triangles congruent?

Yes! If all three sides of one triangle have their lengths equal to the lengths of the corresponding three sides of another triangle, then these two triangles are congruent by the SSS triangle congruence criterion.

What is the formula for an SSS triangle area?

The quickest formula for the area of a triangle with sides a, b, and c is the Heron's formula: Area=√(s(s-a)(s-b)(s-c)), where s is the semi-perimeter of the triangle; that is one-half of its perimeter: s = ½(a+b+c).

How do I calculate a SSS triangle with sides 2 3 4?

Apply the law of cosines to sides 2 and 3 to determine the angle between these sides: γ = acos((2² + 3² - 4²)/(2 × 2 × 3)) =104.48° Apply the law of cosines again to sides a and c to determine the angle β between theses sides. β = acos((2² + 4² - 3²)/(2 × 2 × 4)) =46.57° Compute the remaining angle α as α = 180° - 104.48° - 46.57° = 28.95°.