Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 10.2   b = 15.55   c = 7.8

Area: T = 34.82328583277
Perimeter: p = 33.55
Semiperimeter: s = 16.775

Angle ∠ A = α = 35.04442031498° = 35°2'39″ = 0.61216367287 rad
Angle ∠ B = β = 118.9099298761° = 118°54'33″ = 2.07553587746 rad
Angle ∠ C = γ = 26.04664980891° = 26°2'47″ = 0.45545971503 rad

Height: ha = 6.82880114368
Height: hb = 4.47988242222
Height: hc = 8.92989380327

Median: ma = 11.19442507565
Median: mb = 4.68992829942
Median: mc = 12.55883139792

Inradius: r = 2.07658782908
Circumradius: R = 8.88217953164

Vertex coordinates: A[7.8; 0] B[0; 0] C[-4.93109294872; 8.92989380327]
Centroid: CG[0.95663568376; 2.97663126776]
Coordinates of the circumscribed circle: U[3.9; 7.98797423544]
Coordinates of the inscribed circle: I[1.225; 2.07658782908]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 144.956579685° = 144°57'21″ = 0.61216367287 rad
∠ B' = β' = 61.09107012389° = 61°5'27″ = 2.07553587746 rad
∠ C' = γ' = 153.9543501911° = 153°57'13″ = 0.45545971503 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 = 10.2+15.55+7.8 = 33.55 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33.55 }{ 2 } = 16.78 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.78 * (16.78-10.2)(16.78-15.55)(16.78-7.8) } ; ; T = sqrt{ 1212.63 } = 34.82 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 34.82 }{ 10.2 } = 6.83 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 34.82 }{ 15.55 } = 4.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 34.82 }{ 7.8 } = 8.93 ; ;

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{ 15.55**2+7.8**2-10.2**2 }{ 2 * 15.55 * 7.8 } ) = 35° 2'39" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 10.2**2+7.8**2-15.55**2 }{ 2 * 10.2 * 7.8 } ) = 118° 54'33" ; ; gamma = 180° - alpha - beta = 180° - 35° 2'39" - 118° 54'33" = 26° 2'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 34.82 }{ 16.78 } = 2.08 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 10.2 }{ 2 * sin 35° 2'39" } = 8.88 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.55**2+2 * 7.8**2 - 10.2**2 } }{ 2 } = 11.194 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 7.8**2+2 * 10.2**2 - 15.55**2 } }{ 2 } = 4.689 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 15.55**2+2 * 10.2**2 - 7.8**2 } }{ 2 } = 12.558 ; ;
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