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   b = 71   c = 44

Area: T = 1187.065999743
Perimeter: p = 169
Semiperimeter: s = 84.5

Angle ∠ A = α = 49.46108115181° = 49°27'39″ = 0.86332540117 rad
Angle ∠ B = β = 92.27994106372° = 92°16'46″ = 1.61105795474 rad
Angle ∠ C = γ = 38.26597778448° = 38°15'35″ = 0.66877590945 rad

Height: ha = 43.965518509
Height: hb = 33.43883097868
Height: hc = 53.95772726105

Median: ma = 52.5310943262
Median: mb = 34.14330812904
Median: mc = 59.11442960713

Inradius: r = 14.04880473069
Circumradius: R = 35.52881115456

Vertex coordinates: A[44; 0] B[0; 0] C[-2.14877272727; 53.95772726105]
Centroid: CG[13.95107575758; 17.98657575368]
Coordinates of the circumscribed circle: U[22; 27.89770735023]
Coordinates of the inscribed circle: I[13.5; 14.04880473069]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.5399188482° = 130°32'21″ = 0.86332540117 rad
∠ B' = β' = 87.72105893628° = 87°43'14″ = 1.61105795474 rad
∠ C' = γ' = 141.7440222155° = 141°44'25″ = 0.66877590945 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 = 54 ; ; b = 71 ; ; c = 44 ; ;

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

p = a+b+c = 54+71+44 = 169 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 169 }{ 2 } = 84.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 84.5 * (84.5-54)(84.5-71)(84.5-44) } ; ; T = sqrt{ 1409111.44 } = 1187.06 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1187.06 }{ 54 } = 43.97 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1187.06 }{ 71 } = 33.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1187.06 }{ 44 } = 53.96 ; ;

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**2-71**2-44**2 }{ 2 * 71 * 44 } ) = 49° 27'39" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 71**2-54**2-44**2 }{ 2 * 54 * 44 } ) = 92° 16'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 44**2-54**2-71**2 }{ 2 * 71 * 54 } ) = 38° 15'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1187.06 }{ 84.5 } = 14.05 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 54 }{ 2 * sin 49° 27'39" } = 35.53 ; ;




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