Triangle calculator

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

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

Right scalene triangle.

Sides: a = 1000   b = 87.15657427477   c = 996.1954698092

Area: T = 43412.04444167
Perimeter: p = 2083.355044084
Semiperimeter: s = 1041.675522042

Angle ∠ A = α = 90° = 1.57107963268 rad
Angle ∠ B = β = 5° = 0.08772664626 rad
Angle ∠ C = γ = 85° = 1.48435298642 rad

Height: ha = 86.82440888335
Height: hb = 996.1954698092
Height: hc = 87.15657427477

Median: ma = 500
Median: mb = 997.1477384984
Median: mc = 505.6655000391

Inradius: r = 41.67552204197
Circumradius: R = 500

Vertex coordinates: A[996.1954698092; 0] B[0; 0] C[996.1954698092; 87.15657427477]
Centroid: CG[664.1329798728; 29.05219142492]
Coordinates of the circumscribed circle: U[498.0977349046; 43.57878713738]
Coordinates of the inscribed circle: I[954.5199477672; 41.67552204197]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 90° = 1.57107963268 rad
∠ B' = β' = 175° = 0.08772664626 rad
∠ C' = γ' = 95° = 1.48435298642 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 = 1000 ; ; b = 87.16 ; ; c = 996.19 ; ;

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

p = a+b+c = 1000+87.16+996.19 = 2083.35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2083.35 }{ 2 } = 1041.68 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1041.68 * (1041.68-1000)(1041.68-87.16)(1041.68-996.19) } ; ; T = sqrt{ 1884605600.44 } = 43412.04 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 43412.04 }{ 1000 } = 86.82 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 43412.04 }{ 87.16 } = 996.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 43412.04 }{ 996.19 } = 87.16 ; ;

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{ 1000**2-87.16**2-996.19**2 }{ 2 * 87.16 * 996.19 } ) = 90° ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 87.16**2-1000**2-996.19**2 }{ 2 * 1000 * 996.19 } ) = 5° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 996.19**2-1000**2-87.16**2 }{ 2 * 87.16 * 1000 } ) = 85° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 43412.04 }{ 1041.68 } = 41.68 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 1000 }{ 2 * sin 90° } = 500 ; ;




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

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