Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 60   b = 50   c = 89.47

Area: T = 1422.397737672
Perimeter: p = 199.47
Semiperimeter: s = 99.735

Angle ∠ A = α = 39.48883626795° = 39°29'18″ = 0.6899201945 rad
Angle ∠ B = β = 32.00110340274° = 32°4″ = 0.55985234078 rad
Angle ∠ C = γ = 108.5110603293° = 108°30'38″ = 1.89438673008 rad

Height: ha = 47.41332458907
Height: hb = 56.89658950688
Height: hc = 31.79660741415

Median: ma = 65.97330282009
Median: mb = 71.95444331504
Median: mc = 32.38548695381

Inradius: r = 14.26217674509
Circumradius: R = 47.17656353732

Vertex coordinates: A[89.47; 0] B[0; 0] C[50.88223119481; 31.79660741415]
Centroid: CG[46.78441039827; 10.59986913805]
Coordinates of the circumscribed circle: U[44.735; -14.97773277946]
Coordinates of the inscribed circle: I[49.735; 14.26217674509]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 140.512163732° = 140°30'42″ = 0.6899201945 rad
∠ B' = β' = 147.9998965973° = 147°59'56″ = 0.55985234078 rad
∠ C' = γ' = 71.48993967069° = 71°29'22″ = 1.89438673008 rad

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How did we calculate this triangle?

a = 60 ; ; b = 50 ; ; c = 89.47 ; ;

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

p = a+b+c = 60+50+89.47 = 199.47 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 199.47 }{ 2 } = 99.74 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 99.74 * (99.74-60)(99.74-50)(99.74-89.47) } ; ; T = sqrt{ 2023214.3 } = 1422.4 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1422.4 }{ 60 } = 47.41 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1422.4 }{ 50 } = 56.9 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1422.4 }{ 89.47 } = 31.8 ; ;

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{ 60**2-50**2-89.47**2 }{ 2 * 50 * 89.47 } ) = 39° 29'18" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 50**2-60**2-89.47**2 }{ 2 * 60 * 89.47 } ) = 32° 4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 89.47**2-60**2-50**2 }{ 2 * 50 * 60 } ) = 108° 30'38" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1422.4 }{ 99.74 } = 14.26 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 60 }{ 2 * sin 39° 29'18" } = 47.18 ; ;




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