4 14 15 triangle

Obtuse scalene triangle.

Sides: a = 4   b = 14   c = 15

Area: T = 27.81107443266
Perimeter: p = 33
Semiperimeter: s = 16.5

Angle ∠ A = α = 15.35988855808° = 15°21'32″ = 0.26880631228 rad
Angle ∠ B = β = 67.9765687163° = 67°58'32″ = 1.18663995523 rad
Angle ∠ C = γ = 96.66554272562° = 96°39'56″ = 1.68771299785 rad

Height: ha = 13.90553721633
Height: hb = 3.97329634752
Height: hc = 3.70880992435

Median: ma = 14.37701078632
Median: mb = 8.45657672626
Median: mc = 7.05333679898

Inradius: r = 1.68554996562
Circumradius: R = 7.55110384596

Vertex coordinates: A[15; 0] B[0; 0] C[1.5; 3.70880992435]
Centroid: CG[5.5; 1.23660330812]
Coordinates of the circumscribed circle: U[7.5; -0.87664598212]
Coordinates of the inscribed circle: I[2.5; 1.68554996562]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 164.6411114419° = 164°38'28″ = 0.26880631228 rad
∠ B' = β' = 112.0244312837° = 112°1'28″ = 1.18663995523 rad
∠ C' = γ' = 83.33545727438° = 83°20'4″ = 1.68771299785 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 = 14 ; ; c = 15 ; ;

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

p = a+b+c = 4+14+15 = 33 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 33 }{ 2 } = 16.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 16.5 * (16.5-4)(16.5-14)(16.5-15) } ; ; T = sqrt{ 773.44 } = 27.81 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 27.81 }{ 4 } = 13.91 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 27.81 }{ 14 } = 3.97 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 27.81 }{ 15 } = 3.71 ; ;

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**2-14**2-15**2 }{ 2 * 14 * 15 } ) = 15° 21'32" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 14**2-4**2-15**2 }{ 2 * 4 * 15 } ) = 67° 58'32" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 15**2-4**2-14**2 }{ 2 * 14 * 4 } ) = 96° 39'56" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 27.81 }{ 16.5 } = 1.69 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 4 }{ 2 * sin 15° 21'32" } = 7.55 ; ;




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