10 11 14 triangle

Acute scalene triangle.

Sides: a = 10   b = 11   c = 14

Area: T = 54.6443732486
Perimeter: p = 35
Semiperimeter: s = 17.5

Angle ∠ A = α = 45.20771662976° = 45°12'26″ = 0.78990138974 rad
Angle ∠ B = β = 51.31878125465° = 51°19'4″ = 0.89656647939 rad
Angle ∠ C = γ = 83.47550211559° = 83°28'30″ = 1.45769139623 rad

Height: ha = 10.92987464972
Height: hb = 9.93552240884
Height: hc = 7.8066247498

Median: ma = 11.55442200083
Median: mb = 10.85112672071
Median: mc = 7.84221935707

Inradius: r = 3.12224989992
Circumradius: R = 7.04656387674

Vertex coordinates: A[14; 0] B[0; 0] C[6.25; 7.8066247498]
Centroid: CG[6.75; 2.60220824993]
Coordinates of the circumscribed circle: U[7; 0.8010640769]
Coordinates of the inscribed circle: I[6.5; 3.12224989992]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 134.7932833702° = 134°47'34″ = 0.78990138974 rad
∠ B' = β' = 128.6822187453° = 128°40'56″ = 0.89656647939 rad
∠ C' = γ' = 96.52549788441° = 96°31'30″ = 1.45769139623 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 = 10 ; ; b = 11 ; ; c = 14 ; ;

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

p = a+b+c = 10+11+14 = 35 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 35 }{ 2 } = 17.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 17.5 * (17.5-10)(17.5-11)(17.5-14) } ; ; T = sqrt{ 2985.94 } = 54.64 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 54.64 }{ 10 } = 10.93 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 54.64 }{ 11 } = 9.94 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 54.64 }{ 14 } = 7.81 ; ;

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{ 10**2-11**2-14**2 }{ 2 * 11 * 14 } ) = 45° 12'26" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 11**2-10**2-14**2 }{ 2 * 10 * 14 } ) = 51° 19'4" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 14**2-10**2-11**2 }{ 2 * 11 * 10 } ) = 83° 28'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 54.64 }{ 17.5 } = 3.12 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 45° 12'26" } = 7.05 ; ;




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