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 = 24.68875   b = 66.68875   c = 57.43875

Area: T = 696.0876518009
Perimeter: p = 148.81325
Semiperimeter: s = 74.406625

Angle ∠ A = α = 21.31326657186° = 21°18'46″ = 0.37219761892 rad
Angle ∠ B = β = 100.9549657318° = 100°56'59″ = 1.7621903899 rad
Angle ∠ C = γ = 57.73876769634° = 57°44'16″ = 1.00877125655 rad

Height: ha = 56.39218191805
Height: hb = 20.87660717679
Height: hc = 24.23880506815

Median: ma = 60.99881669166
Median: mb = 29.0255228116
Median: mc = 41.27444600775

Inradius: r = 9.35552156977
Circumradius: R = 33.96220474824

Vertex coordinates: A[57.43875; 0] B[0; 0] C[-4.68993022307; 24.23880506815]
Centroid: CG[17.58327325898; 8.07993502272]
Coordinates of the circumscribed circle: U[28.719875; 18.12988187048]
Coordinates of the inscribed circle: I[7.719875; 9.35552156977]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.6877334281° = 158°41'14″ = 0.37219761892 rad
∠ B' = β' = 79.05503426821° = 79°3'1″ = 1.7621903899 rad
∠ C' = γ' = 122.2622323037° = 122°15'44″ = 1.00877125655 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 = 24.69 ; ; b = 66.69 ; ; c = 57.44 ; ;

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

p = a+b+c = 24.69+66.69+57.44 = 148.81 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 148.81 }{ 2 } = 74.41 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 74.41 * (74.41-24.69)(74.41-66.69)(74.41-57.44) } ; ; T = sqrt{ 484536.44 } = 696.09 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 696.09 }{ 24.69 } = 56.39 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 696.09 }{ 66.69 } = 20.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 696.09 }{ 57.44 } = 24.24 ; ;

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{ 24.69**2-66.69**2-57.44**2 }{ 2 * 66.69 * 57.44 } ) = 21° 18'46" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 66.69**2-24.69**2-57.44**2 }{ 2 * 24.69 * 57.44 } ) = 100° 56'59" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 57.44**2-24.69**2-66.69**2 }{ 2 * 66.69 * 24.69 } ) = 57° 44'16" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 696.09 }{ 74.41 } = 9.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 24.69 }{ 2 * sin 21° 18'46" } = 33.96 ; ;




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