Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 100   b = 90   c = 74.49

Area: T = 3225.546624223
Perimeter: p = 264.49
Semiperimeter: s = 132.245

Angle ∠ A = α = 74.20990056974° = 74°12'32″ = 1.29551914841 rad
Angle ∠ B = β = 60.00110653491° = 60°4″ = 1.0477216145 rad
Angle ∠ C = γ = 45.79899289535° = 45°47'24″ = 0.79991850245 rad

Height: ha = 64.51109248447
Height: hb = 71.6798805383
Height: hc = 86.6033470056

Median: ma = 65.76600186283
Median: mb = 75.82546665011
Median: mc = 87.53774775453

Inradius: r = 24.39106857895
Circumradius: R = 51.96109664265

Vertex coordinates: A[74.49; 0] B[0; 0] C[49.99883897167; 86.6033470056]
Centroid: CG[41.49661299056; 28.8687823352]
Coordinates of the circumscribed circle: U[37.245; 36.23219197253]
Coordinates of the inscribed circle: I[42.245; 24.39106857895]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 105.7910994303° = 105°47'28″ = 1.29551914841 rad
∠ B' = β' = 119.9998934651° = 119°59'56″ = 1.0477216145 rad
∠ C' = γ' = 134.2110071047° = 134°12'36″ = 0.79991850245 rad

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How did we calculate this triangle?

a = 100 ; ; b = 90 ; ; c = 74.49 ; ;

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

p = a+b+c = 100+90+74.49 = 264.49 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 264.49 }{ 2 } = 132.25 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 132.25 * (132.25-100)(132.25-90)(132.25-74.49) } ; ; T = sqrt{ 10404148.56 } = 3225.55 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 3225.55 }{ 100 } = 64.51 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 3225.55 }{ 90 } = 71.68 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 3225.55 }{ 74.49 } = 86.6 ; ;

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+74.49**2-100**2 }{ 2 * 90 * 74.49 } ) = 74° 12'32" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 100**2+74.49**2-90**2 }{ 2 * 100 * 74.49 } ) = 60° 4" ; ; gamma = 180° - alpha - beta = 180° - 74° 12'32" - 60° 4" = 45° 47'24" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 3225.55 }{ 132.25 } = 24.39 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 100 }{ 2 * sin 74° 12'32" } = 51.96 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 74.49**2 - 100**2 } }{ 2 } = 65.76 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 74.49**2+2 * 100**2 - 90**2 } }{ 2 } = 75.825 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 90**2+2 * 100**2 - 74.49**2 } }{ 2 } = 87.537 ; ;
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