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 = 105   b = 38   c = 133

Area: T = 1508.97331608
Perimeter: p = 276
Semiperimeter: s = 138

Angle ∠ A = α = 36.66553494337° = 36°39'55″ = 0.6439931069 rad
Angle ∠ B = β = 12.48105313632° = 12°28'50″ = 0.21878263647 rad
Angle ∠ C = γ = 130.8544119203° = 130°51'15″ = 2.28438352199 rad

Height: ha = 28.74223459199
Height: hb = 79.42196400418
Height: hc = 22.69113257262

Median: ma = 82.52442388635
Median: mb = 118.3054691369
Median: mc = 42.57105297125

Inradius: r = 10.93545881217
Circumradius: R = 87.91990587658

Vertex coordinates: A[133; 0] B[0; 0] C[102.5198796993; 22.69113257262]
Centroid: CG[78.50662656642; 7.56437752421]
Coordinates of the circumscribed circle: U[66.5; -57.51109632528]
Coordinates of the inscribed circle: I[100; 10.93545881217]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 143.3354650566° = 143°20'5″ = 0.6439931069 rad
∠ B' = β' = 167.5199468637° = 167°31'10″ = 0.21878263647 rad
∠ C' = γ' = 49.14658807969° = 49°8'45″ = 2.28438352199 rad

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How did we calculate this triangle?

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

a = 105 ; ; b = 38 ; ; c = 133 ; ;

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

p = a+b+c = 105+38+133 = 276 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 276 }{ 2 } = 138 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 138 * (138-105)(138-38)(138-133) } ; ; T = sqrt{ 2277000 } = 1508.97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1508.97 }{ 105 } = 28.74 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1508.97 }{ 38 } = 79.42 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1508.97 }{ 133 } = 22.69 ; ;

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{ 38**2+133**2-105**2 }{ 2 * 38 * 133 } ) = 36° 39'55" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 105**2+133**2-38**2 }{ 2 * 105 * 133 } ) = 12° 28'50" ; ; gamma = 180° - alpha - beta = 180° - 36° 39'55" - 12° 28'50" = 130° 51'15" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1508.97 }{ 138 } = 10.93 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 105 }{ 2 * sin 36° 39'55" } = 87.92 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 38**2+2 * 133**2 - 105**2 } }{ 2 } = 82.524 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 133**2+2 * 105**2 - 38**2 } }{ 2 } = 118.305 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 38**2+2 * 105**2 - 133**2 } }{ 2 } = 42.571 ; ;
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