Triangle calculator

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

You have entered side b, angle α and angle γ.

Right scalene triangle.

Sides: a = 2.03304167878   b = 97.5   c = 97.52111392075

Area: T = 98.98328184065
Perimeter: p = 197.0521555995
Semiperimeter: s = 98.52657779977

Angle ∠ A = α = 1.193° = 1°11'35″ = 0.0210821778 rad
Angle ∠ B = β = 88.807° = 88°48'25″ = 1.55499745488 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 97.5
Height: hb = 2.03304167878
Height: hc = 2.03299766637

Median: ma = 97.50552852315
Median: mb = 48.79222646772
Median: mc = 48.76105696038

Inradius: r = 1.00546387902
Circumradius: R = 48.76105696037

Vertex coordinates: A[97.52111392075; 0] B[0; 0] C[0.04222738328; 2.03299766637]
Centroid: CG[32.52111376801; 0.67766588879]
Coordinates of the circumscribed circle: U[48.76105696038; -0]
Coordinates of the inscribed circle: I[1.02657779977; 1.00546387902]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 178.807° = 178°48'25″ = 0.0210821778 rad
∠ B' = β' = 91.193° = 91°11'35″ = 1.55499745488 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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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 = 2.03 ; ; b = 97.5 ; ; c = 97.52 ; ;

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

p = a+b+c = 2.03+97.5+97.52 = 197.05 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 197.05 }{ 2 } = 98.53 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 98.53 * (98.53-2.03)(98.53-97.5)(98.53-97.52) } ; ; T = sqrt{ 9797.6 } = 98.98 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 98.98 }{ 2.03 } = 97.5 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 98.98 }{ 97.5 } = 2.03 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 98.98 }{ 97.52 } = 2.03 ; ;

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{ 2.03**2-97.5**2-97.52**2 }{ 2 * 97.5 * 97.52 } ) = 1° 11'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 97.5**2-2.03**2-97.52**2 }{ 2 * 2.03 * 97.52 } ) = 88° 48'25" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 97.52**2-2.03**2-97.5**2 }{ 2 * 97.5 * 2.03 } ) = 90° ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 98.98 }{ 98.53 } = 1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 2.03 }{ 2 * sin 1° 11'35" } = 48.76 ; ;




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