4.2 6.4 7.6 triangle

Acute scalene triangle.

Sides: a = 4.2   b = 6.4   c = 7.6

Area: T = 13.43883592749
Perimeter: p = 18.2
Semiperimeter: s = 9.1

Angle ∠ A = α = 33.54331004217° = 33°32'35″ = 0.58554375437 rad
Angle ∠ B = β = 57.35221825649° = 57°21'8″ = 1.0010984419 rad
Angle ∠ C = γ = 89.10547170134° = 89°6'17″ = 1.55551706909 rad

Height: ha = 6.39992187023
Height: hb = 4.19994872734
Height: hc = 3.53664103355

Median: ma = 6.70444761167
Median: mb = 5.24402290026
Median: mc = 3.85548670535

Inradius: r = 1.47767427775
Circumradius: R = 3.88004639521

Vertex coordinates: A[7.6; 0] B[0; 0] C[2.26657894737; 3.53664103355]
Centroid: CG[3.28985964912; 1.17988034452]
Coordinates of the circumscribed circle: U[3.8; 0.05993822493]
Coordinates of the inscribed circle: I[2.7; 1.47767427775]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.4576899578° = 146°27'25″ = 0.58554375437 rad
∠ B' = β' = 122.6487817435° = 122°38'52″ = 1.0010984419 rad
∠ C' = γ' = 90.89552829866° = 90°53'43″ = 1.55551706909 rad

Calculate another triangle




How did we calculate this triangle?

a = 4.2 ; ; b = 6.4 ; ; c = 7.6 ; ;

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

p = a+b+c = 4.2+6.4+7.6 = 18.2 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 18.2 }{ 2 } = 9.1 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 9.1 * (9.1-4.2)(9.1-6.4)(9.1-7.6) } ; ; T = sqrt{ 180.59 } = 13.44 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 13.44 }{ 4.2 } = 6.4 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 13.44 }{ 6.4 } = 4.2 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 13.44 }{ 7.6 } = 3.54 ; ;

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{ 4.2**2-6.4**2-7.6**2 }{ 2 * 6.4 * 7.6 } ) = 33° 32'35" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 6.4**2-4.2**2-7.6**2 }{ 2 * 4.2 * 7.6 } ) = 57° 21'8" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 7.6**2-4.2**2-6.4**2 }{ 2 * 6.4 * 4.2 } ) = 89° 6'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 13.44 }{ 9.1 } = 1.48 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4.2 }{ 2 * sin 33° 32'35" } = 3.8 ; ;




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