Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 3   b = 7   c = 8

Area: T = 10.39223048454
Perimeter: p = 18
Semiperimeter: s = 9

Angle ∠ A = α = 21.78767892983° = 21°47'12″ = 0.38802512067 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 98.21332107017° = 98°12'48″ = 1.71441438957 rad

Height: ha = 6.92882032303
Height: hb = 2.96992299558
Height: hc = 2.59880762114

Median: ma = 7.36554599313
Median: mb = 4.92444289009
Median: mc = 3.60655512755

Inradius: r = 1.15547005384
Circumradius: R = 4.04114518843

Vertex coordinates: A[8; 0] B[0; 0] C[1.5; 2.59880762114]
Centroid: CG[3.16766666667; 0.86660254038]
Coordinates of the circumscribed circle: U[4; -0.57773502692]
Coordinates of the inscribed circle: I[2; 1.15547005384]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.2133210702° = 158°12'48″ = 0.38802512067 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 81.78767892983° = 81°47'12″ = 1.71441438957 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 = 3+7+8 = 18 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18 }{ 2 } = 9 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9 * (9-3)(9-7)(9-8) } ; ; T = sqrt{ 108 } = 10.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 10.39 }{ 3 } = 6.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 10.39 }{ 7 } = 2.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 10.39 }{ 8 } = 2.6 ; ;

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{ 7**2+8**2-3**2 }{ 2 * 7 * 8 } ) = 21° 47'12" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 3**2+8**2-7**2 }{ 2 * 3 * 8 } ) = 60° ; ; gamma = 180° - alpha - beta = 180° - 21° 47'12" - 60° = 98° 12'48" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 10.39 }{ 9 } = 1.15 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 3 }{ 2 * sin 21° 47'12" } = 4.04 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 7**2+2 * 8**2 - 3**2 } }{ 2 } = 7.365 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 8**2+2 * 3**2 - 7**2 } }{ 2 } = 4.924 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 7**2+2 * 3**2 - 8**2 } }{ 2 } = 3.606 ; ;
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