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 = 38   b = 62   c = 80

Area: T = 1144.72770417
Perimeter: p = 180
Semiperimeter: s = 90

Angle ∠ A = α = 27.48993341573° = 27°29'22″ = 0.48797793902 rad
Angle ∠ B = β = 48.86604895851° = 48°51'38″ = 0.85327764174 rad
Angle ∠ C = γ = 103.6550176258° = 103°39'1″ = 1.8099036846 rad

Height: ha = 60.24987916684
Height: hb = 36.92766787645
Height: hc = 28.61881760425

Median: ma = 69
Median: mb = 54.41550714417
Median: mc = 32.31109888428

Inradius: r = 12.71991893522
Circumradius: R = 41.16326512553

Vertex coordinates: A[80; 0] B[0; 0] C[25; 28.61881760425]
Centroid: CG[35; 9.53993920142]
Coordinates of the circumscribed circle: U[40; -9.71441061536]
Coordinates of the inscribed circle: I[28; 12.71991893522]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.5110665843° = 152°30'38″ = 0.48797793902 rad
∠ B' = β' = 131.1439510415° = 131°8'22″ = 0.85327764174 rad
∠ C' = γ' = 76.35498237424° = 76°20'59″ = 1.8099036846 rad

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How did we calculate this triangle?

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

a = 38 ; ; b = 62 ; ; c = 80 ; ;

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

p = a+b+c = 38+62+80 = 180 ; ;

3. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 180 }{ 2 } = 90 ; ;

4. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 90 * (90-38)(90-62)(90-80) } ; ; T = sqrt{ 1310400 } = 1144.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 1144.73 }{ 38 } = 60.25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 1144.73 }{ 62 } = 36.93 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 1144.73 }{ 80 } = 28.62 ; ;

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{ 62**2+80**2-38**2 }{ 2 * 62 * 80 } ) = 27° 29'22" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 38**2+80**2-62**2 }{ 2 * 38 * 80 } ) = 48° 51'38" ; ; gamma = 180° - alpha - beta = 180° - 27° 29'22" - 48° 51'38" = 103° 39'1" ; ;

7. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 1144.73 }{ 90 } = 12.72 ; ;

8. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 38 }{ 2 * sin 27° 29'22" } = 41.16 ; ;

9. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 62**2+2 * 80**2 - 38**2 } }{ 2 } = 69 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 80**2+2 * 38**2 - 62**2 } }{ 2 } = 54.415 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 62**2+2 * 38**2 - 80**2 } }{ 2 } = 32.311 ; ;
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