Triangle calculator SSS - result

Please enter the triangle sides:


Right scalene triangle.

Sides: a = 1077.98   b = 479.95   c = 1180

Area: T = 258688.2550494
Perimeter: p = 2737.93
Semiperimeter: s = 1368.965

Angle ∠ A = α = 665.9995654595° = 65°59'58″ = 1.15219097222 rad
Angle ∠ B = β = 244.0000404563° = 24° = 0.41988797266 rad
Angle ∠ C = γ = 900.0003940842° = 90°1″ = 1.57108032049 rad

Height: ha = 479.9549999989
Height: hb = 1077.987999997
Height: hc = 438.4554661854

Median: ma = 721.7110316644
Median: mb = 1104.37697024
Median: mc = 589.9976984272

Inradius: r = 188.9666299718
Circumradius: R = 5900.000000014

Vertex coordinates: A[1180; 0] B[0; 0] C[984.7833422839; 438.4554661854]
Centroid: CG[721.594447428; 146.1521553951]
Coordinates of the circumscribed circle: U[590; -0.00440580593]
Coordinates of the inscribed circle: I[889.015; 188.9666299718]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 1144.00043454° = 114°2″ = 1.15219097222 rad
∠ B' = β' = 1565.999959544° = 156° = 0.41988797266 rad
∠ C' = γ' = 909.9996059158° = 89°59'59″ = 1.57108032049 rad

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How did we calculate this triangle?

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

p = a+b+c = 1077.98+479.95+1180 = 2737.93 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 2737.93 }{ 2 } = 1368.97 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 1368.97 * (1368.97-1077.98)(1368.97-479.95)(1368.97-1180) } ; ; T = sqrt{ 66919610943.6 } = 258688.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 258688.25 }{ 1077.98 } = 479.95 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 258688.25 }{ 479.95 } = 1077.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 258688.25 }{ 1180 } = 438.45 ; ;

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{ 479.95**2+1180**2-1077.98**2 }{ 2 * 479.95 * 1180 } ) = 65° 59'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1077.98**2+1180**2-479.95**2 }{ 2 * 1077.98 * 1180 } ) = 24° ; ; gamma = 180° - alpha - beta = 180° - 65° 59'58" - 24° = 90° 1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 258688.25 }{ 1368.97 } = 188.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1077.98 }{ 2 * sin 65° 59'58" } = 590 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 479.95**2+2 * 1180**2 - 1077.98**2 } }{ 2 } = 721.71 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 1180**2+2 * 1077.98**2 - 479.95**2 } }{ 2 } = 1104.37 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 479.95**2+2 * 1077.98**2 - 1180**2 } }{ 2 } = 589.997 ; ;
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