Triangle calculator

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

You have entered side a, b and c.

Right scalene triangle.

Sides: a = 1.73220508076   b = 2.23660679775   c = 2.82884271247

Area: T = 1.93664916731
Perimeter: p = 6.79765459098
Semiperimeter: s = 3.39882729549

Angle ∠ A = α = 37.7611243907° = 37°45'40″ = 0.65990580358 rad
Angle ∠ B = β = 52.2398756093° = 52°14'20″ = 0.9121738291 rad
Angle ∠ C = γ = 90° = 1.57107963268 rad

Height: ha = 2.23660679775
Height: hb = 1.73220508076
Height: hc = 1.36993063938

Median: ma = 2.39879157617
Median: mb = 2.06215528128
Median: mc = 1.41442135624

Inradius: r = 0.57698458302
Circumradius: R = 1.41442135624

Vertex coordinates: A[2.82884271247; 0] B[0; 0] C[1.06106601718; 1.36993063938]
Centroid: CG[1.29663624322; 0.45664354646]
Coordinates of the circumscribed circle: U[1.41442135624; 0]
Coordinates of the inscribed circle: I[1.16222049774; 0.57698458302]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 142.2398756093° = 142°14'20″ = 0.65990580358 rad
∠ B' = β' = 127.7611243907° = 127°45'40″ = 0.9121738291 rad
∠ C' = γ' = 90° = 1.57107963268 rad

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How did we calculate this triangle?

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

a = 1.732 ; ; b = 2.236 ; ; c = 2.828 ; ;

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

p = a+b+c = 1.73+2.24+2.83 = 6.8 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 6.8 }{ 2 } = 3.4 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 3.4 * (3.4-1.73)(3.4-2.24)(3.4-2.83) } ; ; T = sqrt{ 3.75 } = 1.94 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1.94 }{ 1.73 } = 2.24 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1.94 }{ 2.24 } = 1.73 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1.94 }{ 2.83 } = 1.37 ; ;

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{ 2.24**2+2.83**2-1.73**2 }{ 2 * 2.24 * 2.83 } ) = 37° 45'40" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 1.73**2+2.83**2-2.24**2 }{ 2 * 1.73 * 2.83 } ) = 52° 14'20" ; ;
 gamma = 180° - alpha - beta = 180° - 37° 45'40" - 52° 14'20" = 90° ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1.94 }{ 3.4 } = 0.57 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 1.73 }{ 2 * sin 37° 45'40" } = 1.41 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.24**2+2 * 2.83**2 - 1.73**2 } }{ 2 } = 2.398 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.83**2+2 * 1.73**2 - 2.24**2 } }{ 2 } = 2.062 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 2.24**2+2 * 1.73**2 - 2.83**2 } }{ 2 } = 1.414 ; ;
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