Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 70   b = 56   c = 38.86

Area: T = 1086.227695514
Perimeter: p = 164.86
Semiperimeter: s = 82.43

Angle ∠ A = α = 93.34443508868° = 93°20'40″ = 1.62991662611 rad
Angle ∠ B = β = 533.0001958512° = 53°1″ = 0.92550279218 rad
Angle ∠ C = γ = 33.6555453262° = 33°39'20″ = 0.58773984707 rad

Height: ha = 31.03550558612
Height: hb = 38.79438198265
Height: hc = 55.90546297037

Median: ma = 33.13768344897
Median: mb = 49.20441644579
Median: mc = 60.33663497404

Inradius: r = 13.17875683021
Circumradius: R = 35.06597081206

Vertex coordinates: A[38.86; 0] B[0; 0] C[42.1276860525; 55.90546297037]
Centroid: CG[26.9965620175; 18.63548765679]
Coordinates of the circumscribed circle: U[19.43; 29.18331840877]
Coordinates of the inscribed circle: I[26.43; 13.17875683021]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 86.65656491132° = 86°39'20″ = 1.62991662611 rad
∠ B' = β' = 1276.999804149° = 126°59'59″ = 0.92550279218 rad
∠ C' = γ' = 146.3454546738° = 146°20'40″ = 0.58773984707 rad

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How did we calculate this triangle?

a = 70 ; ; b = 56 ; ; c = 38.86 ; ;

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

p = a+b+c = 70+56+38.86 = 164.86 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 164.86 }{ 2 } = 82.43 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 82.43 * (82.43-70)(82.43-56)(82.43-38.86) } ; ; T = sqrt{ 1179889 } = 1086.23 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1086.23 }{ 70 } = 31.04 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1086.23 }{ 56 } = 38.79 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1086.23 }{ 38.86 } = 55.9 ; ;

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{ 56**2+38.86**2-70**2 }{ 2 * 56 * 38.86 } ) = 93° 20'40" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 70**2+38.86**2-56**2 }{ 2 * 70 * 38.86 } ) = 53° 1" ; ; gamma = 180° - alpha - beta = 180° - 93° 20'40" - 53° 1" = 33° 39'20" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1086.23 }{ 82.43 } = 13.18 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 70 }{ 2 * sin 93° 20'40" } = 35.06 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 56**2+2 * 38.86**2 - 70**2 } }{ 2 } = 33.137 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 38.86**2+2 * 70**2 - 56**2 } }{ 2 } = 49.204 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 56**2+2 * 70**2 - 38.86**2 } }{ 2 } = 60.336 ; ;
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