Triangle calculator

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

You have entered side a, b and c.

Acute scalene triangle.

Sides: a = 150   b = 340   c = 369

Area: T = 25495.39220824
Perimeter: p = 859
Semiperimeter: s = 429.5

Angle ∠ A = α = 23.98108075536° = 23°58'51″ = 0.41985440491 rad
Angle ∠ B = β = 67.10884395912° = 67°6'30″ = 1.17112632267 rad
Angle ∠ C = γ = 88.91107528552° = 88°54'39″ = 1.55217853777 rad

Height: ha = 339.9398561099
Height: hb = 149.9732894603
Height: hc = 138.1866406951

Median: ma = 346.7798747907
Median: mb = 224.5677361832
Median: mc = 187.1098925495

Inradius: r = 59.36106334865
Circumradius: R = 184.5333345664

Vertex coordinates: A[369; 0] B[0; 0] C[58.34882384824; 138.1866406951]
Centroid: CG[142.4499412827; 46.06221356503]
Coordinates of the circumscribed circle: U[184.5; 3.50879427181]
Coordinates of the inscribed circle: I[89.5; 59.36106334865]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.0199192446° = 156°1'9″ = 0.41985440491 rad
∠ B' = β' = 112.8921560409° = 112°53'30″ = 1.17112632267 rad
∠ C' = γ' = 91.08992471448° = 91°5'21″ = 1.55217853777 rad

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How did we calculate this triangle?

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

a = 150 ; ; b = 340 ; ; c = 369 ; ;

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

p = a+b+c = 150+340+369 = 859 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 859 }{ 2 } = 429.5 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 429.5 * (429.5-150)(429.5-340)(429.5-369) } ; ; T = sqrt{ 650015017.44 } = 25495.39 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 25495.39 }{ 150 } = 339.94 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 25495.39 }{ 340 } = 149.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 25495.39 }{ 369 } = 138.19 ; ;

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{ 340**2+369**2-150**2 }{ 2 * 340 * 369 } ) = 23° 58'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 150**2+369**2-340**2 }{ 2 * 150 * 369 } ) = 67° 6'30" ; ;
 gamma = 180° - alpha - beta = 180° - 23° 58'51" - 67° 6'30" = 88° 54'39" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 25495.39 }{ 429.5 } = 59.36 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 150 }{ 2 * sin 23° 58'51" } = 184.53 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 340**2+2 * 369**2 - 150**2 } }{ 2 } = 346.779 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 369**2+2 * 150**2 - 340**2 } }{ 2 } = 224.567 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 340**2+2 * 150**2 - 369**2 } }{ 2 } = 187.109 ; ;
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