Isosceles Triangle Calculator
Calculate all properties of an isosceles triangle from the equal side length and base length. This tool computes the area, perimeter, height, base angles, and vertex angle instantly.
An isosceles triangle has two equal sides (called legs) and a third side (called the base). The two angles adjacent to the base are equal (base angles), and the angle between the two equal sides is the vertex angle.
Isosceles Triangle Formulas (equal sides = a, base = b):
- Height: h = sqrt(a^2 - (b/2)^2)
- Area: A = (b x h) / 2 = (b/4) x sqrt(4a^2 - b^2)
- Perimeter: P = 2a + b
- Base Angles: arccos(b / (2a))
- Vertex Angle: 180 - 2 x base angle
The altitude from the vertex to the base bisects both the base and the vertex angle, creating two congruent right triangles. This axis of symmetry is a key property of isosceles triangles.
Isosceles triangles appear in architecture (gable roofs, A-frame buildings), bridge design (truss structures), road signs, and decorative patterns. An equilateral triangle is a special case where the base equals the equal sides.