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 = 15.27   b = 4.94   c = 14.55

Area: T = 35.93110179839
Perimeter: p = 34.76
Semiperimeter: s = 17.38

Angle ∠ A = α = 88.83108384865° = 88°49'51″ = 1.55503906089 rad
Angle ∠ B = β = 18.87112591154° = 18°52'17″ = 0.32993656056 rad
Angle ∠ C = γ = 72.29879023981° = 72°17'52″ = 1.26218364391 rad

Height: ha = 4.70660927287
Height: hb = 14.54769708437
Height: hc = 4.93989715442

Median: ma = 7.73304479172
Median: mb = 14.70883921623
Median: mc = 8.71099153268

Inradius: r = 2.06773773293
Circumradius: R = 7.63765898573

Vertex coordinates: A[14.55; 0] B[0; 0] C[14.44992027491; 4.93989715442]
Centroid: CG[9.66664009164; 1.64663238481]
Coordinates of the circumscribed circle: U[7.275; 2.32220421291]
Coordinates of the inscribed circle: I[12.44; 2.06773773293]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 91.16991615135° = 91°10'9″ = 1.55503906089 rad
∠ B' = β' = 161.1298740885° = 161°7'43″ = 0.32993656056 rad
∠ C' = γ' = 107.7022097602° = 107°42'8″ = 1.26218364391 rad

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How did we calculate this triangle?

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

a = 15.27 ; ; b = 4.94 ; ; c = 14.55 ; ;

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

p = a+b+c = 15.27+4.94+14.55 = 34.76 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 34.76 }{ 2 } = 17.38 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.38 * (17.38-15.27)(17.38-4.94)(17.38-14.55) } ; ; T = sqrt{ 1291.04 } = 35.93 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 35.93 }{ 15.27 } = 4.71 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 35.93 }{ 4.94 } = 14.55 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 35.93 }{ 14.55 } = 4.94 ; ;

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{ 4.94**2+14.55**2-15.27**2 }{ 2 * 4.94 * 14.55 } ) = 88° 49'51" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 15.27**2+14.55**2-4.94**2 }{ 2 * 15.27 * 14.55 } ) = 18° 52'17" ; ;
 gamma = 180° - alpha - beta = 180° - 88° 49'51" - 18° 52'17" = 72° 17'52" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 35.93 }{ 17.38 } = 2.07 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 15.27 }{ 2 * sin 88° 49'51" } = 7.64 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.94**2+2 * 14.55**2 - 15.27**2 } }{ 2 } = 7.73 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 14.55**2+2 * 15.27**2 - 4.94**2 } }{ 2 } = 14.708 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 4.94**2+2 * 15.27**2 - 14.55**2 } }{ 2 } = 8.71 ; ;
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