Math

Isosceles Triangle Calculator

Solve Isosceles Triangles Quickly

An isosceles triangle has two equal sides (legs) and two equal base angles. Enter the leg length and either the base or the apex angle to compute all properties.

Triangle Solver Tips

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Try an Example

Pick a scenario to see how the calculator works, then adjust the values

Right Triangle

Classic 3-4-5 right triangle using SSS mode.

Key values: a = 3 · b = 4 · c = 5

Roof Pitch

Calculate a roof triangle with two sides and a 35-degree pitch angle.

Key values: a = 6 · b = 8 · C = 35°

Equilateral Triangle

A perfect equilateral triangle with all sides equal to 10.

Key values: a = 10 · b = 10 · c = 10

Documentation

This calculator is also known as Isosceles Triangle Calculator.

Read the complete guide

Properties of Isosceles Triangles

An isosceles triangle has: (1) two equal sides (legs), (2) two equal base angles, and (3) one axis of symmetry through the apex and midpoint of the base. The altitude from the apex bisects the base and bisects the apex angle.

Examples

Roofing (Apex Angle)

A roof truss forms an isosceles triangle with equal rafters of 6 m and an apex angle of 40°. Find the span (base) and height.

c = √(36+36-72cos40°) = √(72-55.15) = √16.85 ≈ 4.10 m (span). Height h = ½c ÷ tan(20°) ≈ 5.64 m.

Key takeaway: For roof design, the apex angle directly controls the pitch; steeper pitches shed snow better but use more materials.

Geometry Homework

An isosceles triangle has legs of 13 cm and base 10 cm. Find all angles and height.

cos A = (169+100-169)/(2×13×10) = 0.3846. A ≈ 67.4° (base angles). C = 180-2×67.4 = 45.2° (apex).

Key takeaway: Knowing the equal sides and base is enough to find all angles using the Law of Cosines (SSS mode).

Architecture: Triangular Facade

A triangular facade is isosceles with base 8 m and equal sides 5 m. What is the area and height?

s = 9. Area = √(9×4×4×1) = √144 = 12 m². Height = 2×12/8 = 3 m.

Key takeaway: The altitude of an isosceles triangle from apex to base = 2 × Area / base.

Working with Isosceles Triangles

Use symmetry to simplify calculations:

The altitude from the apex bisects the base, creating two congruent right triangles
If you know the apex angle, the two base angles are each (180° - apex) / 2
For roof trusses, verify the apex angle matches the design pitch before cutting rafters

Frequently Asked Questions about Isosceles Triangle Calculator

What makes a triangle isosceles?

An isosceles triangle has exactly two equal sides (legs) and two equal base angles. If all three sides are equal, it is equilateral (a special case of isosceles).