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

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

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

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

2. Semiperimeter of the triangle

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

3. 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 ; ;

4. 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 ; ;

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{ 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" ; ;

6. Inradius

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

7. Circumradius

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




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

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