18.8 11.6 13.8 triangle

Obtuse scalene triangle.

Sides: a = 18.8   b = 11.6   c = 13.8

Area: T = 79.72435818312
Perimeter: p = 44.2
Semiperimeter: s = 22.1

Angle ∠ A = α = 95.09663350634° = 95°5'47″ = 1.66597441534 rad
Angle ∠ B = β = 37.92215566245° = 37°55'18″ = 0.66218560206 rad
Angle ∠ C = γ = 46.98221083121° = 46°58'56″ = 0.82199924796 rad

Height: ha = 8.48112321097
Height: hb = 13.74554451433
Height: hc = 11.55441422944

Median: ma = 8.61104587567
Median: mb = 15.43769686143
Median: mc = 14.01439216496

Inradius: r = 3.60774018928
Circumradius: R = 9.43773080426

Vertex coordinates: A[13.8; 0] B[0; 0] C[14.83304347826; 11.55441422944]
Centroid: CG[9.54334782609; 3.85113807648]
Coordinates of the circumscribed circle: U[6.9; 6.43883835775]
Coordinates of the inscribed circle: I[10.5; 3.60774018928]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 84.90436649366° = 84°54'13″ = 1.66597441534 rad
∠ B' = β' = 142.0788443375° = 142°4'42″ = 0.66218560206 rad
∠ C' = γ' = 133.0187891688° = 133°1'4″ = 0.82199924796 rad

Calculate another triangle




How did we calculate this triangle?

a = 18.8 ; ; b = 11.6 ; ; c = 13.8 ; ;

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

p = a+b+c = 18.8+11.6+13.8 = 44.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 44.2 }{ 2 } = 22.1 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 22.1 * (22.1-18.8)(22.1-11.6)(22.1-13.8) } ; ; T = sqrt{ 6355.85 } = 79.72 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 79.72 }{ 18.8 } = 8.48 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 79.72 }{ 11.6 } = 13.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 79.72 }{ 13.8 } = 11.55 ; ;

5. 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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 18.8**2-11.6**2-13.8**2 }{ 2 * 11.6 * 13.8 } ) = 95° 5'47" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11.6**2-18.8**2-13.8**2 }{ 2 * 18.8 * 13.8 } ) = 37° 55'18" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 13.8**2-18.8**2-11.6**2 }{ 2 * 11.6 * 18.8 } ) = 46° 58'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 79.72 }{ 22.1 } = 3.61 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 18.8 }{ 2 * sin 95° 5'47" } = 9.44 ; ;




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