Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 76.6   b = 64.28   c = 100

Area: T = 2461.924399655
Perimeter: p = 240.88
Semiperimeter: s = 120.44

Angle ∠ A = α = 49.99660385674° = 49°59'46″ = 0.8732595486 rad
Angle ∠ B = β = 40.0010926664° = 40°3″ = 0.69881478741 rad
Angle ∠ C = γ = 90.00330347686° = 90°11″ = 1.57108492935 rad

Height: ha = 64.28799999098
Height: hb = 76.65999998926
Height: hc = 49.23884799309

Median: ma = 74.82769283079
Median: mb = 83.07110563313
Median: mc = 49.9977391932

Inradius: r = 20.44110826681
Circumradius: R = 500.0000000701

Vertex coordinates: A[100; 0] B[0; 0] C[58.6788208; 49.23884799309]
Centroid: CG[52.8932736; 16.41328266436]
Coordinates of the circumscribed circle: U[50; -0.00326483352]
Coordinates of the inscribed circle: I[56.16; 20.44110826681]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 130.0043961433° = 130°14″ = 0.8732595486 rad
∠ B' = β' = 139.9999073336° = 139°59'57″ = 0.69881478741 rad
∠ C' = γ' = 89.99769652314° = 89°59'49″ = 1.57108492935 rad

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How did we calculate this triangle?

a = 76.6 ; ; b = 64.28 ; ; c = 100 ; ;

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

p = a+b+c = 76.6+64.28+100 = 240.88 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 240.88 }{ 2 } = 120.44 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 120.44 * (120.44-76.6)(120.44-64.28)(120.44-100) } ; ; T = sqrt{ 6061069.76 } = 2461.92 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 2461.92 }{ 76.6 } = 64.28 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 2461.92 }{ 64.28 } = 76.6 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 2461.92 }{ 100 } = 49.24 ; ;

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{ 64.28**2+100**2-76.6**2 }{ 2 * 64.28 * 100 } ) = 49° 59'46" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 76.6**2+100**2-64.28**2 }{ 2 * 76.6 * 100 } ) = 40° 3" ; ; gamma = 180° - alpha - beta = 180° - 49° 59'46" - 40° 3" = 90° 11" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 2461.92 }{ 120.44 } = 20.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 76.6 }{ 2 * sin 49° 59'46" } = 50 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 64.28**2+2 * 100**2 - 76.6**2 } }{ 2 } = 74.827 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 100**2+2 * 76.6**2 - 64.28**2 } }{ 2 } = 83.071 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 64.28**2+2 * 76.6**2 - 100**2 } }{ 2 } = 49.997 ; ;
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