14 26 30 triangle

Obtuse scalene triangle.

Sides: a = 14   b = 26   c = 30

Area: T = 181.8655334795
Perimeter: p = 70
Semiperimeter: s = 35

Angle ∠ A = α = 27.7965772496° = 27°47'45″ = 0.48551277482 rad
Angle ∠ B = β = 60° = 1.04771975512 rad
Angle ∠ C = γ = 92.2044227504° = 92°12'15″ = 1.60992673542 rad

Height: ha = 25.98107621135
Height: hb = 13.99896411381
Height: hc = 12.1244355653

Median: ma = 27.18545544381
Median: mb = 19.46879223339
Median: mc = 14.52658390463

Inradius: r = 5.19661524227
Circumradius: R = 15.01111069989

Vertex coordinates: A[30; 0] B[0; 0] C[7; 12.1244355653]
Centroid: CG[12.33333333333; 4.04114518843]
Coordinates of the circumscribed circle: U[15; -0.57773502692]
Coordinates of the inscribed circle: I[9; 5.19661524227]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 152.2044227504° = 152°12'15″ = 0.48551277482 rad
∠ B' = β' = 120° = 1.04771975512 rad
∠ C' = γ' = 87.7965772496° = 87°47'45″ = 1.60992673542 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 = 14 ; ; b = 26 ; ; c = 30 ; ;

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

p = a+b+c = 14+26+30 = 70 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 70 }{ 2 } = 35 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 35 * (35-14)(35-26)(35-30) } ; ; T = sqrt{ 33075 } = 181.87 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 181.87 }{ 14 } = 25.98 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 181.87 }{ 26 } = 13.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 181.87 }{ 30 } = 12.12 ; ;

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{ 14**2-26**2-30**2 }{ 2 * 26 * 30 } ) = 27° 47'45" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 26**2-14**2-30**2 }{ 2 * 14 * 30 } ) = 60° ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 30**2-14**2-26**2 }{ 2 * 26 * 14 } ) = 92° 12'15" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 181.87 }{ 35 } = 5.2 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 14 }{ 2 * sin 27° 47'45" } = 15.01 ; ;




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