Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 64.69   b = 64.88   c = 25.28

Area: T = 803.1222420975
Perimeter: p = 154.85
Semiperimeter: s = 77.425

Angle ∠ A = α = 78.32769882281° = 78°19'37″ = 1.36770638378 rad
Angle ∠ B = β = 79.17216951234° = 79°10'18″ = 1.38218067543 rad
Angle ∠ C = γ = 22.50113166485° = 22°30'5″ = 0.39327220616 rad

Height: ha = 24.83298785276
Height: hb = 24.75771646416
Height: hc = 63.53881662164

Median: ma = 37.12220604897
Median: mb = 36.87325324598
Median: mc = 63.54400318697

Inradius: r = 10.37329082464
Circumradius: R = 33.02880794201

Vertex coordinates: A[25.28; 0] B[0; 0] C[12.15330874209; 63.53881662164]
Centroid: CG[12.4787695807; 21.17993887388]
Coordinates of the circumscribed circle: U[12.64; 30.51436761171]
Coordinates of the inscribed circle: I[12.545; 10.37329082464]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 101.6733011772° = 101°40'23″ = 1.36770638378 rad
∠ B' = β' = 100.8288304877° = 100°49'42″ = 1.38218067543 rad
∠ C' = γ' = 157.4998683351° = 157°29'55″ = 0.39327220616 rad

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How did we calculate this triangle?

a = 64.69 ; ; b = 64.88 ; ; c = 25.28 ; ;

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

p = a+b+c = 64.69+64.88+25.28 = 154.85 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 154.85 }{ 2 } = 77.43 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 77.43 * (77.43-64.69)(77.43-64.88)(77.43-25.28) } ; ; T = sqrt{ 645005.62 } = 803.12 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 803.12 }{ 64.69 } = 24.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 803.12 }{ 64.88 } = 24.76 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 803.12 }{ 25.28 } = 63.54 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 64.88**2+25.28**2-64.69**2 }{ 2 * 64.88 * 25.28 } ) = 78° 19'37" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 64.69**2+25.28**2-64.88**2 }{ 2 * 64.69 * 25.28 } ) = 79° 10'18" ; ; gamma = 180° - alpha - beta = 180° - 78° 19'37" - 79° 10'18" = 22° 30'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 803.12 }{ 77.43 } = 10.37 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 64.69 }{ 2 * sin 78° 19'37" } = 33.03 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 64.88**2+2 * 25.28**2 - 64.69**2 } }{ 2 } = 37.122 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 25.28**2+2 * 64.69**2 - 64.88**2 } }{ 2 } = 36.873 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 64.88**2+2 * 64.69**2 - 25.28**2 } }{ 2 } = 63.54 ; ;
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