5.7 10.2 9.8 triangle

Acute scalene triangle.

Sides: a = 5.7   b = 10.2   c = 9.8

Area: T = 27.25106861152
Perimeter: p = 25.7
Semiperimeter: s = 12.85

Angle ∠ A = α = 33.0410506482° = 33°2'26″ = 0.57766656246 rad
Angle ∠ B = β = 77.33774374776° = 77°20'15″ = 1.3549792919 rad
Angle ∠ C = γ = 69.62220560404° = 69°37'19″ = 1.21551341099 rad

Height: ha = 9.5621644251
Height: hb = 5.34332717873
Height: hc = 5.56113645133

Median: ma = 9.58773614723
Median: mb = 6.18550626513
Median: mc = 6.65224431602

Inradius: r = 2.12106759623
Circumradius: R = 5.22771344434

Vertex coordinates: A[9.8; 0] B[0; 0] C[1.24994897959; 5.56113645133]
Centroid: CG[3.68331632653; 1.85437881711]
Coordinates of the circumscribed circle: U[4.9; 1.82201468319]
Coordinates of the inscribed circle: I[2.65; 2.12106759623]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.9599493518° = 146°57'34″ = 0.57766656246 rad
∠ B' = β' = 102.6632562522° = 102°39'45″ = 1.3549792919 rad
∠ C' = γ' = 110.378794396° = 110°22'41″ = 1.21551341099 rad

Calculate another triangle




How did we calculate this triangle?

a = 5.7 ; ; b = 10.2 ; ; c = 9.8 ; ;

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

p = a+b+c = 5.7+10.2+9.8 = 25.7 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 25.7 }{ 2 } = 12.85 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 12.85 * (12.85-5.7)(12.85-10.2)(12.85-9.8) } ; ; T = sqrt{ 742.6 } = 27.25 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.25 }{ 5.7 } = 9.56 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.25 }{ 10.2 } = 5.34 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.25 }{ 9.8 } = 5.56 ; ;

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{ 5.7**2-10.2**2-9.8**2 }{ 2 * 10.2 * 9.8 } ) = 33° 2'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10.2**2-5.7**2-9.8**2 }{ 2 * 5.7 * 9.8 } ) = 77° 20'15" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 9.8**2-5.7**2-10.2**2 }{ 2 * 10.2 * 5.7 } ) = 69° 37'19" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.25 }{ 12.85 } = 2.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 5.7 }{ 2 * sin 33° 2'26" } = 5.23 ; ;




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