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

Calculate another triangle




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{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 6**2-25**2-28**2 }{ 2 * 25 * 28 } ) = 11° 16'15" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-6**2-28**2 }{ 2 * 6 * 28 } ) = 54° 31'28" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 28**2-6**2-25**2 }{ 2 * 25 * 6 } ) = 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 ; ;




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