Triangle calculator

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

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 32   b = 38   c = 46

Area: T = 601.5987872337
Perimeter: p = 116
Semiperimeter: s = 58

Angle ∠ A = α = 43.49878286118° = 43°29'52″ = 0.75991803267 rad
Angle ∠ B = β = 54.82442119874° = 54°49'27″ = 0.9576863009 rad
Angle ∠ C = γ = 81.67879594008° = 81°40'41″ = 1.42655493179 rad

Height: ha = 37.6599867021
Height: hb = 31.66330459125
Height: hc = 26.1566429232

Median: ma = 39.03884425919
Median: mb = 34.77106773014
Median: mc = 26.55218360947

Inradius: r = 10.37223771093
Circumradius: R = 23.24547630602

Vertex coordinates: A[46; 0] B[0; 0] C[18.43547826087; 26.1566429232]
Centroid: CG[21.47882608696; 8.7198809744]
Coordinates of the circumscribed circle: U[23; 3.36443736008]
Coordinates of the inscribed circle: I[20; 10.37223771093]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 136.5022171388° = 136°30'8″ = 0.75991803267 rad
∠ B' = β' = 125.1765788013° = 125°10'33″ = 0.9576863009 rad
∠ C' = γ' = 98.32220405992° = 98°19'19″ = 1.42655493179 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 = 32 ; ; b = 38 ; ; c = 46 ; ;

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

p = a+b+c = 32+38+46 = 116 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 116 }{ 2 } = 58 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 58 * (58-32)(58-38)(58-46) } ; ; T = sqrt{ 361920 } = 601.6 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 601.6 }{ 32 } = 37.6 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 601.6 }{ 38 } = 31.66 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 601.6 }{ 46 } = 26.16 ; ;

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{ 32**2-38**2-46**2 }{ 2 * 38 * 46 } ) = 43° 29'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 38**2-32**2-46**2 }{ 2 * 32 * 46 } ) = 54° 49'27" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 46**2-32**2-38**2 }{ 2 * 38 * 32 } ) = 81° 40'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 601.6 }{ 58 } = 10.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 32 }{ 2 * sin 43° 29'52" } = 23.24 ; ;




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