Triangle calculator SSS - result

Please enter the triangle sides:


Obtuse scalene triangle.

Sides: a = 11.7   b = 6.71   c = 5.1

Area: T = 4.65990489855
Perimeter: p = 23.51
Semiperimeter: s = 11.755

Angle ∠ A = α = 164.1999311579° = 164°11'58″ = 2.86658186166 rad
Angle ∠ B = β = 8.98441085527° = 8°59'3″ = 0.15768022746 rad
Angle ∠ C = γ = 6.81765798684° = 6°49' = 0.11989717624 rad

Height: ha = 0.796641863
Height: hb = 1.38986882222
Height: hc = 1.82770780335

Median: ma = 1.13877829318
Median: mb = 8.37881844692
Median: mc = 9.19899156688

Inradius: r = 0.39663461493
Circumradius: R = 21.48443040525

Vertex coordinates: A[5.1; 0] B[0; 0] C[11.55664607843; 1.82770780335]
Centroid: CG[5.55221535948; 0.60990260112]
Coordinates of the circumscribed circle: U[2.55; 21.3322435881]
Coordinates of the inscribed circle: I[5.045; 0.39663461493]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 15.80106884211° = 15°48'2″ = 2.86658186166 rad
∠ B' = β' = 171.0165891447° = 171°57″ = 0.15768022746 rad
∠ C' = γ' = 173.1833420132° = 173°11' = 0.11989717624 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 = 11.7+6.71+5.1 = 23.51 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 23.51 }{ 2 } = 11.76 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.76 * (11.76-11.7)(11.76-6.71)(11.76-5.1) } ; ; T = sqrt{ 21.71 } = 4.66 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 4.66 }{ 11.7 } = 0.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 4.66 }{ 6.71 } = 1.39 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 4.66 }{ 5.1 } = 1.83 ; ;

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{ 6.71**2+5.1**2-11.7**2 }{ 2 * 6.71 * 5.1 } ) = 164° 11'58" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11.7**2+5.1**2-6.71**2 }{ 2 * 11.7 * 5.1 } ) = 8° 59'3" ; ; gamma = 180° - alpha - beta = 180° - 164° 11'58" - 8° 59'3" = 6° 49' ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 4.66 }{ 11.76 } = 0.4 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11.7 }{ 2 * sin 164° 11'58" } = 21.48 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.71**2+2 * 5.1**2 - 11.7**2 } }{ 2 } = 1.138 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 5.1**2+2 * 11.7**2 - 6.71**2 } }{ 2 } = 8.378 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 6.71**2+2 * 11.7**2 - 5.1**2 } }{ 2 } = 9.19 ; ;
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