Triangle calculator

Please enter what you know about the triangle:
Symbols definition of ABC triangle

You have entered side a, b and c.

Obtuse scalene triangle.

Sides: a = 24.3   b = 13.45   c = 11.6

Area: T = 36.85217603411
Perimeter: p = 49.35
Semiperimeter: s = 24.675

Angle ∠ A = α = 151.8109937537° = 151°48'36″ = 2.65495832473 rad
Angle ∠ B = β = 15.15773798302° = 15°9'27″ = 0.2654546184 rad
Angle ∠ C = γ = 13.03326826329° = 13°1'58″ = 0.22774632223 rad

Height: ha = 3.03330666947
Height: hb = 5.48798156641
Height: hc = 6.35437517829

Median: ma = 3.17994260488
Median: mb = 17.81328991183
Median: mc = 18.76331620469

Inradius: r = 1.49334857281
Circumradius: R = 25.72198432647

Vertex coordinates: A[11.6; 0] B[0; 0] C[23.45546336207; 6.35437517829]
Centroid: CG[11.68548778736; 2.1187917261]
Coordinates of the circumscribed circle: U[5.8; 25.05773409914]
Coordinates of the inscribed circle: I[11.225; 1.49334857281]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 28.19900624631° = 28°11'24″ = 2.65495832473 rad
∠ B' = β' = 164.843262017° = 164°50'33″ = 0.2654546184 rad
∠ C' = γ' = 166.9677317367° = 166°58'2″ = 0.22774632223 rad

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How did we calculate this triangle?

1. Input data entered: side a, b and c.

a = 24.3 ; ; b = 13.45 ; ; c = 11.6 ; ;

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

p = a+b+c = 24.3+13.45+11.6 = 49.35 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 49.35 }{ 2 } = 24.68 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.68 * (24.68-24.3)(24.68-13.45)(24.68-11.6) } ; ; T = sqrt{ 1358.05 } = 36.85 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 36.85 }{ 24.3 } = 3.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 36.85 }{ 13.45 } = 5.48 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 36.85 }{ 11.6 } = 6.35 ; ;

6. 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{ 13.45**2+11.6**2-24.3**2 }{ 2 * 13.45 * 11.6 } ) = 151° 48'36" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 24.3**2+11.6**2-13.45**2 }{ 2 * 24.3 * 11.6 } ) = 15° 9'27" ; ;
 gamma = 180° - alpha - beta = 180° - 151° 48'36" - 15° 9'27" = 13° 1'58" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 36.85 }{ 24.68 } = 1.49 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 24.3 }{ 2 * sin 151° 48'36" } = 25.72 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.45**2+2 * 11.6**2 - 24.3**2 } }{ 2 } = 3.179 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 11.6**2+2 * 24.3**2 - 13.45**2 } }{ 2 } = 17.813 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 13.45**2+2 * 24.3**2 - 11.6**2 } }{ 2 } = 18.763 ; ;
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