Triangle calculator SSS - result

Please enter the triangle sides:


Acute scalene triangle.

Sides: a = 3.61   b = 6.4   c = 6.32

Area: T = 11.0055070405
Perimeter: p = 16.33
Semiperimeter: s = 8.165

Angle ∠ A = α = 32.96772072651° = 32°58'2″ = 0.5755386312 rad
Angle ∠ B = β = 74.73440166305° = 74°44'2″ = 1.30443546534 rad
Angle ∠ C = γ = 72.29987761044° = 72°17'56″ = 1.26218516882 rad

Height: ha = 6.09769919141
Height: hb = 3.43990845016
Height: hc = 3.48326172168

Median: ma = 6.09986207457
Median: mb = 4.03107877642
Median: mc = 4.12443726796

Inradius: r = 1.34878347097
Circumradius: R = 3.31770455669

Vertex coordinates: A[6.32; 0] B[0; 0] C[0.95105142405; 3.48326172168]
Centroid: CG[2.42435047468; 1.16108724056]
Coordinates of the circumscribed circle: U[3.16; 1.00985590179]
Coordinates of the inscribed circle: I[1.765; 1.34878347097]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 147.0332792735° = 147°1'58″ = 0.5755386312 rad
∠ B' = β' = 105.266598337° = 105°15'58″ = 1.30443546534 rad
∠ C' = γ' = 107.7011223896° = 107°42'4″ = 1.26218516882 rad

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How did we calculate this triangle?

a = 3.61 ; ; b = 6.4 ; ; c = 6.32 ; ;

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

p = a+b+c = 3.61+6.4+6.32 = 16.33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 16.33 }{ 2 } = 8.17 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 8.17 * (8.17-3.61)(8.17-6.4)(8.17-6.32) } ; ; T = sqrt{ 121.11 } = 11.01 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 11.01 }{ 3.61 } = 6.1 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 11.01 }{ 6.4 } = 3.44 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 11.01 }{ 6.32 } = 3.48 ; ;

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{ 6.4**2+6.32**2-3.61**2 }{ 2 * 6.4 * 6.32 } ) = 32° 58'2" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3.61**2+6.32**2-6.4**2 }{ 2 * 3.61 * 6.32 } ) = 74° 44'2" ; ; gamma = 180° - alpha - beta = 180° - 32° 58'2" - 74° 44'2" = 72° 17'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 11.01 }{ 8.17 } = 1.35 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3.61 }{ 2 * sin 32° 58'2" } = 3.32 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.4**2+2 * 6.32**2 - 3.61**2 } }{ 2 } = 6.099 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.32**2+2 * 3.61**2 - 6.4**2 } }{ 2 } = 4.031 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.4**2+2 * 3.61**2 - 6.32**2 } }{ 2 } = 4.124 ; ;
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