Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 7.91   b = 5.27   c = 4.7

Area: T = 11.977025307
Perimeter: p = 17.88
Semiperimeter: s = 8.94

Angle ∠ A = α = 104.8610933357° = 104°51'39″ = 1.83301685438 rad
Angle ∠ B = β = 40.08877550725° = 40°5'16″ = 0.76996633157 rad
Angle ∠ C = γ = 35.05113115701° = 35°3'5″ = 0.6121760794 rad

Height: ha = 3.02766126599
Height: hb = 4.54327905389
Height: hc = 5.09437247106

Median: ma = 3.04878558037
Median: mb = 5.94985985745
Median: mc = 6.29766657844

Inradius: r = 1.33989544821
Circumradius: R = 4.0921868168

Vertex coordinates: A[4.7; 0] B[0; 0] C[6.05216170213; 5.09437247106]
Centroid: CG[3.58438723404; 1.69879082369]
Coordinates of the circumscribed circle: U[2.35; 3.35497589621]
Coordinates of the inscribed circle: I[3.67; 1.33989544821]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 75.13990666426° = 75°8'21″ = 1.83301685438 rad
∠ B' = β' = 139.9122244928° = 139°54'44″ = 0.76996633157 rad
∠ C' = γ' = 144.949868843° = 144°56'55″ = 0.6121760794 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 = 7.91+5.27+4.7 = 17.88 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 17.88 }{ 2 } = 8.94 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.94 * (8.94-7.91)(8.94-5.27)(8.94-4.7) } ; ; T = sqrt{ 143.29 } = 11.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.97 }{ 7.91 } = 3.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.97 }{ 5.27 } = 4.54 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.97 }{ 4.7 } = 5.09 ; ;

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{ 5.27**2+4.7**2-7.91**2 }{ 2 * 5.27 * 4.7 } ) = 104° 51'39" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 7.91**2+4.7**2-5.27**2 }{ 2 * 7.91 * 4.7 } ) = 40° 5'16" ; ; gamma = 180° - alpha - beta = 180° - 104° 51'39" - 40° 5'16" = 35° 3'5" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.97 }{ 8.94 } = 1.34 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 7.91 }{ 2 * sin 104° 51'39" } = 4.09 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.27**2+2 * 4.7**2 - 7.91**2 } }{ 2 } = 3.048 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.7**2+2 * 7.91**2 - 5.27**2 } }{ 2 } = 5.949 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.27**2+2 * 7.91**2 - 4.7**2 } }{ 2 } = 6.297 ; ;
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