Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 4.12   b = 3.61   c = 6.32

Area: T = 7.0099485556
Perimeter: p = 14.05
Semiperimeter: s = 7.025

Angle ∠ A = α = 37.91325129827° = 37°54'45″ = 0.66216981793 rad
Angle ∠ B = β = 32.57545160747° = 32°34'28″ = 0.56985325577 rad
Angle ∠ C = γ = 109.5132970943° = 109°30'47″ = 1.91113619166 rad

Height: ha = 3.40326628912
Height: hb = 3.88333714992
Height: hc = 2.21881916316

Median: ma = 4.71663174193
Median: mb = 5.021999751
Median: mc = 2.24400111607

Inradius: r = 0.99877915382
Circumradius: R = 3.35325507418

Vertex coordinates: A[6.32; 0] B[0; 0] C[3.47218908228; 2.21881916316]
Centroid: CG[3.26439636076; 0.73993972105]
Coordinates of the circumscribed circle: U[3.16; -1.12198198409]
Coordinates of the inscribed circle: I[3.415; 0.99877915382]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.0877487017° = 142°5'15″ = 0.66216981793 rad
∠ B' = β' = 147.4255483925° = 147°25'32″ = 0.56985325577 rad
∠ C' = γ' = 70.48770290574° = 70°29'13″ = 1.91113619166 rad

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How did we calculate this triangle?

a = 4.12 ; ; b = 3.61 ; ; c = 6.32 ; ;

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

p = a+b+c = 4.12+3.61+6.32 = 14.05 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 14.05 }{ 2 } = 7.03 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 7.03 * (7.03-4.12)(7.03-3.61)(7.03-6.32) } ; ; T = sqrt{ 49.13 } = 7.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 7.01 }{ 4.12 } = 3.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 7.01 }{ 3.61 } = 3.88 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 7.01 }{ 6.32 } = 2.22 ; ;

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{ 3.61**2+6.32**2-4.12**2 }{ 2 * 3.61 * 6.32 } ) = 37° 54'45" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 4.12**2+6.32**2-3.61**2 }{ 2 * 4.12 * 6.32 } ) = 32° 34'28" ; ; gamma = 180° - alpha - beta = 180° - 37° 54'45" - 32° 34'28" = 109° 30'47" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 7.01 }{ 7.03 } = 1 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 4.12 }{ 2 * sin 37° 54'45" } = 3.35 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.61**2+2 * 6.32**2 - 4.12**2 } }{ 2 } = 4.716 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.32**2+2 * 4.12**2 - 3.61**2 } }{ 2 } = 5.02 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 3.61**2+2 * 4.12**2 - 6.32**2 } }{ 2 } = 2.24 ; ;
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