Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 115   b = 90   c = 92.34

Area: T = 4067.346628284
Perimeter: p = 297.34
Semiperimeter: s = 148.67

Angle ∠ A = α = 78.19904710873° = 78°11'26″ = 1.36546811642 rad
Angle ∠ B = β = 509.9999162262° = 50° = 0.87326631639 rad
Angle ∠ C = γ = 51.81096126865° = 51°48'35″ = 0.90442483256 rad

Height: ha = 70.73664570928
Height: hb = 90.3855472952
Height: hc = 88.09550028772

Median: ma = 70.76107786842
Median: mb = 94.07988913625
Median: mc = 92.36224983421

Inradius: r = 27.3588218086
Circumradius: R = 58.74334000906

Vertex coordinates: A[92.34; 0] B[0; 0] C[73.92107039203; 88.09550028772]
Centroid: CG[55.42202346401; 29.36550009591]
Coordinates of the circumscribed circle: U[46.17; 36.32196662183]
Coordinates of the inscribed circle: I[58.67; 27.3588218086]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 101.8109528913° = 101°48'34″ = 1.36546811642 rad
∠ B' = β' = 1300.000083774° = 130° = 0.87326631639 rad
∠ C' = γ' = 128.1990387313° = 128°11'25″ = 0.90442483256 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 = 115+90+92.34 = 297.34 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 297.34 }{ 2 } = 148.67 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 148.67 * (148.67-115)(148.67-90)(148.67-92.34) } ; ; T = sqrt{ 16543305.78 } = 4067.35 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4067.35 }{ 115 } = 70.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4067.35 }{ 90 } = 90.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4067.35 }{ 92.34 } = 88.1 ; ;

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{ 90**2+92.34**2-115**2 }{ 2 * 90 * 92.34 } ) = 78° 11'26" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 115**2+92.34**2-90**2 }{ 2 * 115 * 92.34 } ) = 50° ; ; gamma = 180° - alpha - beta = 180° - 78° 11'26" - 50° = 51° 48'35" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4067.35 }{ 148.67 } = 27.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 115 }{ 2 * sin 78° 11'26" } = 58.74 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 92.34**2 - 115**2 } }{ 2 } = 70.761 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 92.34**2+2 * 115**2 - 90**2 } }{ 2 } = 94.079 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 115**2 - 92.34**2 } }{ 2 } = 92.362 ; ;
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