9.3 4.6 12.2 triangle

Obtuse scalene triangle.

Sides: a = 9.3   b = 4.6   c = 12.2

Area: T = 18.748816241
Perimeter: p = 26.1
Semiperimeter: s = 13.05

Angle ∠ A = α = 41.92440935815° = 41°55'27″ = 0.73217134689 rad
Angle ∠ B = β = 19.29879463721° = 19°17'53″ = 0.33768127031 rad
Angle ∠ C = γ = 118.7787960046° = 118°46'41″ = 2.07330664816 rad

Height: ha = 4.03218628839
Height: hb = 8.15113749608
Height: hc = 3.07334692475

Median: ma = 7.96109986811
Median: mb = 10.60107075236
Median: mc = 4.07661501444

Inradius: r = 1.43766407977
Circumradius: R = 6.96595620705

Vertex coordinates: A[12.2; 0] B[0; 0] C[8.77774590164; 3.07334692475]
Centroid: CG[6.99224863388; 1.02444897492]
Coordinates of the circumscribed circle: U[6.1; -3.355044836]
Coordinates of the inscribed circle: I[8.45; 1.43766407977]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 138.0765906419° = 138°4'33″ = 0.73217134689 rad
∠ B' = β' = 160.7022053628° = 160°42'7″ = 0.33768127031 rad
∠ C' = γ' = 61.22220399536° = 61°13'19″ = 2.07330664816 rad

Calculate another triangle




How did we calculate this triangle?

a = 9.3 ; ; b = 4.6 ; ; c = 12.2 ; ;

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

p = a+b+c = 9.3+4.6+12.2 = 26.1 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26.1 }{ 2 } = 13.05 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13.05 * (13.05-9.3)(13.05-4.6)(13.05-12.2) } ; ; T = sqrt{ 351.49 } = 18.75 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.75 }{ 9.3 } = 4.03 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.75 }{ 4.6 } = 8.15 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.75 }{ 12.2 } = 3.07 ; ;

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{ 9.3**2-4.6**2-12.2**2 }{ 2 * 4.6 * 12.2 } ) = 41° 55'27" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.6**2-9.3**2-12.2**2 }{ 2 * 9.3 * 12.2 } ) = 19° 17'53" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12.2**2-9.3**2-4.6**2 }{ 2 * 4.6 * 9.3 } ) = 118° 46'41" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.75 }{ 13.05 } = 1.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 9.3 }{ 2 * sin 41° 55'27" } = 6.96 ; ;




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