Triangle calculator

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

You have entered side c, angle α and angle β.

Right scalene triangle.

Sides: a = 0.12994095226   b = 0.03334936491   c = 0.125

Area: T = 0.00220933531
Perimeter: p = 0.28879031716
Semiperimeter: s = 0.14439515858

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 15° = 0.26217993878 rad
Angle ∠ C = γ = 75° = 1.3098996939 rad

Height: ha = 0.03223523806
Height: hb = 0.125
Height: hc = 0.03334936491

Median: ma = 0.06547047613
Median: mb = 0.12661168352
Median: mc = 0.07109089171

Inradius: r = 0.01545420633
Circumradius: R = 0.06547047613

Vertex coordinates: A[0.125; 0] B[0; 0] C[0.125; 0.03334936491]
Centroid: CG[0.08333333333; 0.01111645497]
Coordinates of the circumscribed circle: U[0.06325; 0.01767468245]
Coordinates of the inscribed circle: I[0.11104579367; 0.01545420633]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 165° = 0.26217993878 rad
∠ C' = γ' = 105° = 1.3098996939 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 = 0.13 ; ; b = 0.03 ; ; c = 0.13 ; ;

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

p = a+b+c = 0.13+0.03+0.13 = 0.29 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 0.29 }{ 2 } = 0.14 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 0.14 * (0.14-0.13)(0.14-0.03)(0.14-0.13) } ; ; 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 }{ 0.13 } = 0.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 0 }{ 0.03 } = 0.13 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 0 }{ 0.13 } = 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{ 0.13**2-0.03**2-0.13**2 }{ 2 * 0.03 * 0.13 } ) = 90° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 0.03**2-0.13**2-0.13**2 }{ 2 * 0.13 * 0.13 } ) = 15° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 0.13**2-0.13**2-0.03**2 }{ 2 * 0.03 * 0.13 } ) = 75° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 0 }{ 0.14 } = 0.01 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 0.13 }{ 2 * sin 90° } = 0.06 ; ;




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

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