6 25 28 triangle

Obtuse scalene triangle.

Sides: a = 6   b = 25   c = 28

Area: T = 68.40664141729
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 11.27108312847° = 11°16'15″ = 0.19767131154 rad
Angle ∠ B = β = 54.52443339139° = 54°31'28″ = 0.95216291493 rad
Angle ∠ C = γ = 114.2054834801° = 114°12'17″ = 1.9933250389 rad

Height: ha = 22.80221380576
Height: hb = 5.47325131338
Height: hc = 4.88661724409

Median: ma = 26.37223339885
Median: mb = 15.93295323221
Median: mc = 11.59774135047

Inradius: r = 2.31988614974
Circumradius: R = 15.34994378078

Vertex coordinates: A[28; 0] B[0; 0] C[3.48221428571; 4.88661724409]
Centroid: CG[10.4944047619; 1.6298724147]
Coordinates of the circumscribed circle: U[14; -6.29332695012]
Coordinates of the inscribed circle: I[4.5; 2.31988614974]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 168.7299168715° = 168°43'45″ = 0.19767131154 rad
∠ B' = β' = 125.4765666086° = 125°28'32″ = 0.95216291493 rad
∠ C' = γ' = 65.79551651985° = 65°47'43″ = 1.9933250389 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 = 6 ; ; b = 25 ; ; c = 28 ; ;

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

p = a+b+c = 6+25+28 = 59 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 59 }{ 2 } = 29.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 29.5 * (29.5-6)(29.5-25)(29.5-28) } ; ; T = sqrt{ 4679.44 } = 68.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 68.41 }{ 6 } = 22.8 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 68.41 }{ 25 } = 5.47 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 68.41 }{ 28 } = 4.89 ; ;

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{ b**2+c**2-a**2 }{ 2bc } ) = arccos( fraction{ 25**2+28**2-6**2 }{ 2 * 25 * 28 } ) = 11° 16'15" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 6**2+28**2-25**2 }{ 2 * 6 * 28 } ) = 54° 31'28" ; ; gamma = 180° - alpha - beta = 180° - 11° 16'15" - 54° 31'28" = 114° 12'17" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 68.41 }{ 29.5 } = 2.32 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 6 }{ 2 * sin 11° 16'15" } = 15.35 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 28**2 - 6**2 } }{ 2 } = 26.372 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 28**2+2 * 6**2 - 25**2 } }{ 2 } = 15.93 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 6**2 - 28**2 } }{ 2 } = 11.597 ; ;
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