Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 220.61   b = 280.61   c = 230

Area: T = 24719.99436515
Perimeter: p = 731.22
Semiperimeter: s = 365.61

Angle ∠ A = α = 49.99989629881° = 49°59'56″ = 0.87326465267 rad
Angle ∠ B = β = 77.00107926658° = 77°3″ = 1.34439173587 rad
Angle ∠ C = γ = 533.0002443461° = 53°1″ = 0.92550287682 rad

Height: ha = 224.1065830665
Height: hb = 176.1887546071
Height: hc = 214.9566466535

Median: ma = 231.6332884162
Median: mb = 176.3498782318
Median: mc = 224.6788374794

Inradius: r = 67.61330129142
Circumradius: R = 143.9955137941

Vertex coordinates: A[230; 0] B[0; 0] C[49.62334782609; 214.9566466535]
Centroid: CG[93.2087826087; 71.65221555117]
Coordinates of the circumscribed circle: U[115; 86.65879468404]
Coordinates of the inscribed circle: I[85; 67.61330129142]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.0011037012° = 130°4″ = 0.87326465267 rad
∠ B' = β' = 102.9999207334° = 102°59'57″ = 1.34439173587 rad
∠ C' = γ' = 1276.999755654° = 126°59'59″ = 0.92550287682 rad

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How did we calculate this triangle?

a = 220.61 ; ; b = 280.61 ; ; c = 230 ; ;

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

p = a+b+c = 220.61+280.61+230 = 731.22 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 731.22 }{ 2 } = 365.61 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 365.61 * (365.61-220.61)(365.61-280.61)(365.61-230) } ; ; T = sqrt{ 611078086.13 } = 24719.99 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 24719.99 }{ 220.61 } = 224.11 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 24719.99 }{ 280.61 } = 176.19 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 24719.99 }{ 230 } = 214.96 ; ;

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{ 280.61**2+230**2-220.61**2 }{ 2 * 280.61 * 230 } ) = 49° 59'56" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 220.61**2+230**2-280.61**2 }{ 2 * 220.61 * 230 } ) = 77° 3" ; ; gamma = 180° - alpha - beta = 180° - 49° 59'56" - 77° 3" = 53° 1" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 24719.99 }{ 365.61 } = 67.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 220.61 }{ 2 * sin 49° 59'56" } = 144 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 280.61**2+2 * 230**2 - 220.61**2 } }{ 2 } = 231.633 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 230**2+2 * 220.61**2 - 280.61**2 } }{ 2 } = 176.349 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 280.61**2+2 * 220.61**2 - 230**2 } }{ 2 } = 224.678 ; ;
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