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?

Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

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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