20.8 15.7 12.4 triangle

Obtuse scalene triangle.

Sides: a = 20.8   b = 15.7   c = 12.4

Area: T = 97.00326086956
Perimeter: p = 48.9
Semiperimeter: s = 24.45

Angle ∠ A = α = 94.77218240809° = 94°46'19″ = 1.65440803683 rad
Angle ∠ B = β = 48.78105658324° = 48°46'50″ = 0.85113814848 rad
Angle ∠ C = γ = 36.44876100867° = 36°26'51″ = 0.63661308005 rad

Height: ha = 9.3277173913
Height: hb = 12.3577020216
Height: hc = 15.64655820477

Median: ma = 9.59898383719
Median: mb = 15.21876706496
Median: mc = 17.35329536391

Inradius: r = 3.96773868587
Circumradius: R = 10.43661729402

Vertex coordinates: A[12.4; 0] B[0; 0] C[13.70660483871; 15.64655820477]
Centroid: CG[8.7022016129; 5.21551940159]
Coordinates of the circumscribed circle: U[6.2; 8.39548618594]
Coordinates of the inscribed circle: I[8.75; 3.96773868587]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 85.22881759191° = 85°13'41″ = 1.65440803683 rad
∠ B' = β' = 131.2199434168° = 131°13'10″ = 0.85113814848 rad
∠ C' = γ' = 143.5522389913° = 143°33'9″ = 0.63661308005 rad

Calculate another triangle




How did we calculate this triangle?

a = 20.8 ; ; b = 15.7 ; ; c = 12.4 ; ;

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

p = a+b+c = 20.8+15.7+12.4 = 48.9 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 48.9 }{ 2 } = 24.45 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 24.45 * (24.45-20.8)(24.45-15.7)(24.45-12.4) } ; ; T = sqrt{ 9409.51 } = 97 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 97 }{ 20.8 } = 9.33 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 97 }{ 15.7 } = 12.36 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 97 }{ 12.4 } = 15.65 ; ;

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{ 20.8**2-15.7**2-12.4**2 }{ 2 * 15.7 * 12.4 } ) = 94° 46'19" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 15.7**2-20.8**2-12.4**2 }{ 2 * 20.8 * 12.4 } ) = 48° 46'50" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12.4**2-20.8**2-15.7**2 }{ 2 * 15.7 * 20.8 } ) = 36° 26'51" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 97 }{ 24.45 } = 3.97 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 20.8 }{ 2 * sin 94° 46'19" } = 10.44 ; ;




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