Triangle calculator

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

You have entered side a, b and angle β.

Acute scalene triangle.

Sides: a = 15.4   b = 25.8   c = 27.25875591413

Area: T = 194.6600319381
Perimeter: p = 68.45875591413
Semiperimeter: s = 34.22987795707

Angle ∠ A = α = 33.60330112752° = 33°36'11″ = 0.58664831853 rad
Angle ∠ B = β = 68° = 1.18768238914 rad
Angle ∠ C = γ = 78.39769887248° = 78°23'49″ = 1.36882855769 rad

Height: ha = 25.27327687507
Height: hb = 15.0855296076
Height: hc = 14.27986313603

Median: ma = 25.39771901039
Median: mb = 17.9990477069
Median: mc = 16.29989682929

Inradius: r = 5.6855283607
Circumradius: R = 13.91330981805

Vertex coordinates: A[27.25875591413; 0] B[0; 0] C[5.76989415386; 14.27986313603]
Centroid: CG[11.009883356; 4.76595437868]
Coordinates of the circumscribed circle: U[13.62987795707; 2.79883331459]
Coordinates of the inscribed circle: I[8.42987795707; 5.6855283607]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.3976988725° = 146°23'49″ = 0.58664831853 rad
∠ B' = β' = 112° = 1.18768238914 rad
∠ C' = γ' = 101.6033011275° = 101°36'11″ = 1.36882855769 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 = 15.4 ; ; b = 25.8 ; ; c = 27.26 ; ;

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

p = a+b+c = 15.4+25.8+27.26 = 68.46 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 68.46 }{ 2 } = 34.23 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 34.23 * (34.23-15.4)(34.23-25.8)(34.23-27.26) } ; ; T = sqrt{ 37869.28 } = 194.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 194.6 }{ 15.4 } = 25.27 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 194.6 }{ 25.8 } = 15.09 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 194.6 }{ 27.26 } = 14.28 ; ;

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{ 15.4**2-25.8**2-27.26**2 }{ 2 * 25.8 * 27.26 } ) = 33° 36'11" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25.8**2-15.4**2-27.26**2 }{ 2 * 15.4 * 27.26 } ) = 68° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27.26**2-15.4**2-25.8**2 }{ 2 * 25.8 * 15.4 } ) = 78° 23'49" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 194.6 }{ 34.23 } = 5.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15.4 }{ 2 * sin 33° 36'11" } = 13.91 ; ;




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