Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, c and angle α.

Right scalene triangle.

Sides: a = 0.03   b = 0.05219615242   c = 0.06

Area: T = 0.00107794229
Perimeter: p = 0.14219615242
Semiperimeter: s = 0.07109807621

Angle ∠ A = α = 30° = 0.52435987756 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 0.05219615242
Height: hb = 0.03
Height: hc = 0.02659807621

Median: ma = 0.05440832691
Median: mb = 0.04396862697
Median: mc = 0.03

Inradius: r = 0.01109807621
Circumradius: R = 0.03

Vertex coordinates: A[0.06; 0] B[0; 0] C[0.015; 0.02659807621]
Centroid: CG[0.025; 0.0098660254]
Coordinates of the circumscribed circle: U[0.03; 0]
Coordinates of the inscribed circle: I[0.01990192379; 0.01109807621]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 150° = 0.52435987756 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 90° = 1.57107963268 rad

Calculate another triangle




How did we calculate this triangle?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 0.03 ; ; b = 0.05 ; ; c = 0.06 ; ;

1. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 0.03+0.05+0.06 = 0.14 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.14 }{ 2 } = 0.07 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.07 * (0.07-0.03)(0.07-0.05)(0.07-0.06) } ; ; T = sqrt{ 0 } = 0 ; ;

4. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 0 }{ 0.03 } = 0.05 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0 }{ 0.05 } = 0.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0 }{ 0.06 } = 0.03 ; ;

5. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 0.03**2-0.05**2-0.06**2 }{ 2 * 0.05 * 0.06 } ) = 30° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 0.05**2-0.03**2-0.06**2 }{ 2 * 0.03 * 0.06 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.06**2-0.03**2-0.05**2 }{ 2 * 0.05 * 0.03 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0 }{ 0.07 } = 0.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.03 }{ 2 * sin 30° } = 0.03 ; ;




Look also our friend's collection of math examples and problems:

See more informations about triangles or more information about solving triangles.