Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 9   b = 16   c = 23

Area: T = 53.666563146
Perimeter: p = 48
Semiperimeter: s = 24

Angle ∠ A = α = 16.95774262942° = 16°57'27″ = 0.29659629215 rad
Angle ∠ B = β = 31.232225881° = 31°13'56″ = 0.54551057491 rad
Angle ∠ C = γ = 131.8110314896° = 131°48'37″ = 2.3010523983 rad

Height: ha = 11.926569588
Height: hb = 6.70882039325
Height: hc = 4.66765766487

Median: ma = 19.29437813816
Median: mb = 15.52441746963
Median: mc = 6.02107972894

Inradius: r = 2.23660679775
Circumradius: R = 15.42988690447

Vertex coordinates: A[23; 0] B[0; 0] C[7.69656521739; 4.66765766487]
Centroid: CG[10.2321884058; 1.55655255496]
Coordinates of the circumscribed circle: U[11.5; -10.28659126965]
Coordinates of the inscribed circle: I[8; 2.23660679775]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 163.0432573706° = 163°2'33″ = 0.29659629215 rad
∠ B' = β' = 148.768774119° = 148°46'4″ = 0.54551057491 rad
∠ C' = γ' = 48.19896851042° = 48°11'23″ = 2.3010523983 rad

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How did we calculate this triangle?

a = 9 ; ; b = 16 ; ; c = 23 ; ;

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

p = a+b+c = 9+16+23 = 48 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48 }{ 2 } = 24 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24 * (24-9)(24-16)(24-23) } ; ; T = sqrt{ 2880 } = 53.67 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 53.67 }{ 9 } = 11.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 53.67 }{ 16 } = 6.71 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 53.67 }{ 23 } = 4.67 ; ;

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{ 16**2+23**2-9**2 }{ 2 * 16 * 23 } ) = 16° 57'27" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 9**2+23**2-16**2 }{ 2 * 9 * 23 } ) = 31° 13'56" ; ; gamma = 180° - alpha - beta = 180° - 16° 57'27" - 31° 13'56" = 131° 48'37" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 53.67 }{ 24 } = 2.24 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 9 }{ 2 * sin 16° 57'27" } = 15.43 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 23**2 - 9**2 } }{ 2 } = 19.294 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 23**2+2 * 9**2 - 16**2 } }{ 2 } = 15.524 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 16**2+2 * 9**2 - 23**2 } }{ 2 } = 6.021 ; ;
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