7 25 27 triangle

Obtuse scalene triangle.

Sides: a = 7   b = 25   c = 27

Area: T = 86.41328896635
Perimeter: p = 59
Semiperimeter: s = 29.5

Angle ∠ A = α = 14.8355111582° = 14°50'6″ = 0.2598921542 rad
Angle ∠ B = β = 66.12437922694° = 66°7'26″ = 1.1544077889 rad
Angle ∠ C = γ = 99.04110961486° = 99°2'28″ = 1.72985932226 rad

Height: ha = 24.68993970467
Height: hb = 6.91330311731
Height: hc = 6.40109547899

Median: ma = 25.78327461687
Median: mb = 15.25661463024
Median: mc = 12.44398553046

Inradius: r = 2.92992504971
Circumradius: R = 13.6769835653

Vertex coordinates: A[27; 0] B[0; 0] C[2.83333333333; 6.40109547899]
Centroid: CG[9.94444444444; 2.13436515966]
Coordinates of the circumscribed circle: U[13.5; -2.14881170312]
Coordinates of the inscribed circle: I[4.5; 2.92992504971]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 165.1654888418° = 165°9'54″ = 0.2598921542 rad
∠ B' = β' = 113.8766207731° = 113°52'34″ = 1.1544077889 rad
∠ C' = γ' = 80.95989038514° = 80°57'32″ = 1.72985932226 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 = 7 ; ; b = 25 ; ; c = 27 ; ;

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

p = a+b+c = 7+25+27 = 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 * (29.5-7)(29.5-25)(29.5-27) } ; ; T = sqrt{ 7467.19 } = 86.41 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 86.41 }{ 7 } = 24.69 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 86.41 }{ 25 } = 6.91 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 86.41 }{ 27 } = 6.4 ; ;

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{ 7**2-25**2-27**2 }{ 2 * 25 * 27 } ) = 14° 50'6" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-7**2-27**2 }{ 2 * 7 * 27 } ) = 66° 7'26" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-7**2-25**2 }{ 2 * 25 * 7 } ) = 99° 2'28" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 86.41 }{ 29.5 } = 2.93 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 7 }{ 2 * sin 14° 50'6" } = 13.67 ; ;




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