14.9 23.8 36.9 triangle

Obtuse scalene triangle.

Sides: a = 14.9   b = 23.8   c = 36.9

Area: T = 104.4365683557
Perimeter: p = 75.6
Semiperimeter: s = 37.8

Angle ∠ A = α = 13.75987896448° = 13°45'32″ = 0.24401361804 rad
Angle ∠ B = β = 22.32773250026° = 22°19'38″ = 0.39896853345 rad
Angle ∠ C = γ = 143.9143885353° = 143°54'50″ = 2.51217711387 rad

Height: ha = 14.0188212558
Height: hb = 8.77661078619
Height: hc = 5.66604706535

Median: ma = 30.14217069855
Median: mb = 25.4999019589
Median: mc = 7.33663819421

Inradius: r = 2.76328487713
Circumradius: R = 31.32442503767

Vertex coordinates: A[36.9; 0] B[0; 0] C[13.78329268293; 5.66604706535]
Centroid: CG[16.89443089431; 1.88768235512]
Coordinates of the circumscribed circle: U[18.45; -25.31441494359]
Coordinates of the inscribed circle: I[14; 2.76328487713]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 166.2411210355° = 166°14'28″ = 0.24401361804 rad
∠ B' = β' = 157.6732674997° = 157°40'22″ = 0.39896853345 rad
∠ C' = γ' = 36.08661146473° = 36°5'10″ = 2.51217711387 rad

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How did we calculate this triangle?

a = 14.9 ; ; b = 23.8 ; ; c = 36.9 ; ;

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

p = a+b+c = 14.9+23.8+36.9 = 75.6 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 75.6 }{ 2 } = 37.8 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 37.8 * (37.8-14.9)(37.8-23.8)(37.8-36.9) } ; ; T = sqrt{ 10906.81 } = 104.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 104.44 }{ 14.9 } = 14.02 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 104.44 }{ 23.8 } = 8.78 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 104.44 }{ 36.9 } = 5.66 ; ;

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{ 14.9**2-23.8**2-36.9**2 }{ 2 * 23.8 * 36.9 } ) = 13° 45'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 23.8**2-14.9**2-36.9**2 }{ 2 * 14.9 * 36.9 } ) = 22° 19'38" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 36.9**2-14.9**2-23.8**2 }{ 2 * 23.8 * 14.9 } ) = 143° 54'50" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 104.44 }{ 37.8 } = 2.76 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14.9 }{ 2 * sin 13° 45'32" } = 31.32 ; ;




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