Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 50   b = 60   c = 77.78

Area: T = 1499.947734837
Perimeter: p = 187.78
Semiperimeter: s = 93.89

Angle ∠ A = α = 40.00221393016° = 40°8″ = 0.69881690387 rad
Angle ∠ B = β = 50.47879247335° = 50°28'41″ = 0.88110059862 rad
Angle ∠ C = γ = 89.52199359648° = 89°31'12″ = 1.56224176288 rad

Height: ha = 59.99878939349
Height: hb = 49.99882449457
Height: hc = 38.56989727018

Median: ma = 64.80663592559
Median: mb = 58.0943581401
Median: mc = 39.2121833673

Inradius: r = 15.97655815142
Circumradius: R = 38.89113651291

Vertex coordinates: A[77.78; 0] B[0; 0] C[31.81987734636; 38.56989727018]
Centroid: CG[36.53329244879; 12.85663242339]
Coordinates of the circumscribed circle: U[38.89; 0.32658551919]
Coordinates of the inscribed circle: I[33.89; 15.97655815142]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 139.9987860698° = 139°59'52″ = 0.69881690387 rad
∠ B' = β' = 129.5222075266° = 129°31'19″ = 0.88110059862 rad
∠ C' = γ' = 90.48800640352° = 90°28'48″ = 1.56224176288 rad

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How did we calculate this triangle?

a = 50 ; ; b = 60 ; ; c = 77.78 ; ;

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

p = a+b+c = 50+60+77.78 = 187.78 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 187.78 }{ 2 } = 93.89 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 93.89 * (93.89-50)(93.89-60)(93.89-77.78) } ; ; T = sqrt{ 2249842.05 } = 1499.95 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1499.95 }{ 50 } = 60 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1499.95 }{ 60 } = 50 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1499.95 }{ 77.78 } = 38.57 ; ;

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{ 50**2-60**2-77.78**2 }{ 2 * 60 * 77.78 } ) = 40° 8" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 60**2-50**2-77.78**2 }{ 2 * 50 * 77.78 } ) = 50° 28'41" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 77.78**2-50**2-60**2 }{ 2 * 60 * 50 } ) = 89° 31'12" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1499.95 }{ 93.89 } = 15.98 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 50 }{ 2 * sin 40° 8" } = 38.89 ; ;

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