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 = 16.06   b = 37.59   c = 29.65

Area: T = 227.87547922
Perimeter: p = 83.3
Semiperimeter: s = 41.65

Angle ∠ A = α = 24.13664713134° = 24°8'11″ = 0.42112608942 rad
Angle ∠ B = β = 106.8444012161° = 106°50'38″ = 1.86547797983 rad
Angle ∠ C = γ = 49.02195165256° = 49°1'10″ = 0.85655519611 rad

Height: ha = 28.37879317808
Height: hb = 12.12442241128
Height: hc = 15.37109809241

Median: ma = 32.88774504941
Median: mb = 14.67221172637
Median: mc = 24.81330051586

Inradius: r = 5.47111834862
Circumradius: R = 19.63875040403

Vertex coordinates: A[29.65; 0] B[0; 0] C[-4.65436593592; 15.37109809241]
Centroid: CG[8.33221135469; 5.1243660308]
Coordinates of the circumscribed circle: U[14.825; 12.87883127751]
Coordinates of the inscribed circle: I[4.06; 5.47111834862]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.8643528687° = 155°51'49″ = 0.42112608942 rad
∠ B' = β' = 73.1565987839° = 73°9'22″ = 1.86547797983 rad
∠ C' = γ' = 130.9880483474° = 130°58'50″ = 0.85655519611 rad

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How did we calculate this triangle?

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

a = 16.06 ; ; b = 37.59 ; ; c = 29.65 ; ;

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

p = a+b+c = 16.06+37.59+29.65 = 83.3 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 83.3 }{ 2 } = 41.65 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 41.65 * (41.65-16.06)(41.65-37.59)(41.65-29.65) } ; ; T = sqrt{ 51926.92 } = 227.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 227.87 }{ 16.06 } = 28.38 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 227.87 }{ 37.59 } = 12.12 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 227.87 }{ 29.65 } = 15.37 ; ;

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{ 37.59**2+29.65**2-16.06**2 }{ 2 * 37.59 * 29.65 } ) = 24° 8'11" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 16.06**2+29.65**2-37.59**2 }{ 2 * 16.06 * 29.65 } ) = 106° 50'38" ; ;
 gamma = 180° - alpha - beta = 180° - 24° 8'11" - 106° 50'38" = 49° 1'10" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 227.87 }{ 41.65 } = 5.47 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 16.06 }{ 2 * sin 24° 8'11" } = 19.64 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 37.59**2+2 * 29.65**2 - 16.06**2 } }{ 2 } = 32.887 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 29.65**2+2 * 16.06**2 - 37.59**2 } }{ 2 } = 14.672 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 37.59**2+2 * 16.06**2 - 29.65**2 } }{ 2 } = 24.813 ; ;
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