4 10 12 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 10   c = 12

Area: T = 18.73549939952
Perimeter: p = 26
Semiperimeter: s = 13

Angle ∠ A = α = 18.19548723388° = 18°11'42″ = 0.31875604293 rad
Angle ∠ B = β = 51.31878125465° = 51°19'4″ = 0.89656647939 rad
Angle ∠ C = γ = 110.4877315115° = 110°29'14″ = 1.92883674304 rad

Height: ha = 9.36774969976
Height: hb = 3.7476998799
Height: hc = 3.12224989992

Median: ma = 10.86327804912
Median: mb = 7.41661984871
Median: mc = 4.69904157598

Inradius: r = 1.44111533842
Circumradius: R = 6.40551261522

Vertex coordinates: A[12; 0] B[0; 0] C[2.5; 3.12224989992]
Centroid: CG[4.83333333333; 1.04108329997]
Coordinates of the circumscribed circle: U[6; -2.24217941533]
Coordinates of the inscribed circle: I[3; 1.44111533842]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 161.8055127661° = 161°48'18″ = 0.31875604293 rad
∠ B' = β' = 128.6822187453° = 128°40'56″ = 0.89656647939 rad
∠ C' = γ' = 69.51326848853° = 69°30'46″ = 1.92883674304 rad

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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 ; ; b = 10 ; ; c = 12 ; ;

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

p = a+b+c = 4+10+12 = 26 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 26 }{ 2 } = 13 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 13 * (13-4)(13-10)(13-12) } ; ; T = sqrt{ 351 } = 18.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18.73 }{ 4 } = 9.37 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18.73 }{ 10 } = 3.75 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18.73 }{ 12 } = 3.12 ; ;

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**2-10**2-12**2 }{ 2 * 10 * 12 } ) = 18° 11'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-4**2-12**2 }{ 2 * 4 * 12 } ) = 51° 19'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 12**2-4**2-10**2 }{ 2 * 10 * 4 } ) = 110° 29'14" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18.73 }{ 13 } = 1.44 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 18° 11'42" } = 6.41 ; ;




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