8 10 14 triangle

Obtuse scalene triangle.

Sides: a = 8   b = 10   c = 14

Area: T = 39.19218358845
Perimeter: p = 32
Semiperimeter: s = 16

Angle ∠ A = α = 34.048773237° = 34°2'52″ = 0.59442450327 rad
Angle ∠ B = β = 44.41553085972° = 44°24'55″ = 0.77551933733 rad
Angle ∠ C = γ = 101.5376959033° = 101°32'13″ = 1.77221542476 rad

Height: ha = 9.79879589711
Height: hb = 7.83883671769
Height: hc = 5.59988336978

Median: ma = 11.48991252931
Median: mb = 10.2476950766
Median: mc = 5.74545626465

Inradius: r = 2.44994897428
Circumradius: R = 7.14443450831

Vertex coordinates: A[14; 0] B[0; 0] C[5.71442857143; 5.59988336978]
Centroid: CG[6.57114285714; 1.86662778993]
Coordinates of the circumscribed circle: U[7; -1.42988690166]
Coordinates of the inscribed circle: I[6; 2.44994897428]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 145.952226763° = 145°57'8″ = 0.59442450327 rad
∠ B' = β' = 135.5854691403° = 135°35'5″ = 0.77551933733 rad
∠ C' = γ' = 78.46330409672° = 78°27'47″ = 1.77221542476 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 = 8 ; ; b = 10 ; ; c = 14 ; ;

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

p = a+b+c = 8+10+14 = 32 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 32 }{ 2 } = 16 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16 * (16-8)(16-10)(16-14) } ; ; T = sqrt{ 1536 } = 39.19 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 39.19 }{ 8 } = 9.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 39.19 }{ 10 } = 7.84 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 39.19 }{ 14 } = 5.6 ; ;

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{ 8**2-10**2-14**2 }{ 2 * 10 * 14 } ) = 34° 2'52" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 10**2-8**2-14**2 }{ 2 * 8 * 14 } ) = 44° 24'55" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-8**2-10**2 }{ 2 * 10 * 8 } ) = 101° 32'13" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 39.19 }{ 16 } = 2.45 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 8 }{ 2 * sin 34° 2'52" } = 7.14 ; ;




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