Triangle calculator

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

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 54.1   b = 262.94   c = 214

Area: T = 2731.615465549
Perimeter: p = 531.04
Semiperimeter: s = 265.52

Angle ∠ A = α = 5.57216820542° = 5°34'18″ = 0.09772441967 rad
Angle ∠ B = β = 151.8433117634° = 151°50'35″ = 2.65501623492 rad
Angle ∠ C = γ = 22.5855200312° = 22°35'7″ = 0.39441861077 rad

Height: ha = 100.9843905933
Height: hb = 20.77774751312
Height: hc = 25.52991089299

Median: ma = 238.1911140263
Median: mb = 84.1255169242
Median: mc = 156.799007239

Inradius: r = 10.28877924657
Circumradius: R = 278.605459288

Vertex coordinates: A[214; 0] B[0; 0] C[-47.69877420561; 25.52991089299]
Centroid: CG[55.43440859813; 8.51097029766]
Coordinates of the circumscribed circle: U[107; 257.2388253714]
Coordinates of the inscribed circle: I[2.58; 10.28877924657]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 174.4288317946° = 174°25'42″ = 0.09772441967 rad
∠ B' = β' = 28.15768823662° = 28°9'25″ = 2.65501623492 rad
∠ C' = γ' = 157.4154799688° = 157°24'53″ = 0.39441861077 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 54.1 ; ; b = 262.94 ; ; c = 214 ; ;


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 = 54.1 ; ; b = 262.94 ; ; c = 214 ; ; : Nr. 1

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

p = a+b+c = 54.1+262.94+214 = 531.04 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 531.04 }{ 2 } = 265.52 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 265.52 * (265.52-54.1)(265.52-262.94)(265.52-214) } ; ; T = sqrt{ 7461718.63 } = 2731.61 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2731.61 }{ 54.1 } = 100.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2731.61 }{ 262.94 } = 20.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2731.61 }{ 214 } = 25.53 ; ;

6. 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{ 54.1**2-262.94**2-214**2 }{ 2 * 262.94 * 214 } ) = 5° 34'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 262.94**2-54.1**2-214**2 }{ 2 * 54.1 * 214 } ) = 151° 50'35" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 214**2-54.1**2-262.94**2 }{ 2 * 262.94 * 54.1 } ) = 22° 35'7" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2731.61 }{ 265.52 } = 10.29 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 54.1 }{ 2 * sin 5° 34'18" } = 278.6 ; ;




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