10 25 27 triangle

Obtuse scalene triangle.

Sides: a = 10   b = 25   c = 27

Area: T = 124.9965999936
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 21.73877297313° = 21°44'16″ = 0.37993949557 rad
Angle ∠ B = β = 67.80438991432° = 67°48'14″ = 1.18334012857 rad
Angle ∠ C = γ = 90.45883711255° = 90°27'30″ = 1.57987964121 rad

Height: ha = 24.99991999872
Height: hb = 10.9996799949
Height: hc = 9.25989629582

Median: ma = 25.53442906696
Median: mb = 16.077015868
Median: mc = 13.42657215821

Inradius: r = 4.03221290302
Circumradius: R = 13.55004320207

Vertex coordinates: A[27; 0] B[0; 0] C[3.77877777778; 9.25989629582]
Centroid: CG[10.25992592593; 3.08663209861]
Coordinates of the circumscribed circle: U[13.5; -0.10880034562]
Coordinates of the inscribed circle: I[6; 4.03221290302]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 158.2622270269° = 158°15'44″ = 0.37993949557 rad
∠ B' = β' = 112.1966100857° = 112°11'46″ = 1.18334012857 rad
∠ C' = γ' = 89.54216288745° = 89°32'30″ = 1.57987964121 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 = 10 ; ; b = 25 ; ; c = 27 ; ;

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

p = a+b+c = 10+25+27 = 62 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 62 }{ 2 } = 31 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31 * (31-10)(31-25)(31-27) } ; ; T = sqrt{ 15624 } = 125 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 125 }{ 10 } = 25 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 125 }{ 25 } = 10 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 125 }{ 27 } = 9.26 ; ;

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{ 10**2-25**2-27**2 }{ 2 * 25 * 27 } ) = 21° 44'16" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 25**2-10**2-27**2 }{ 2 * 10 * 27 } ) = 67° 48'14" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-10**2-25**2 }{ 2 * 25 * 10 } ) = 90° 27'30" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 125 }{ 31 } = 4.03 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10 }{ 2 * sin 21° 44'16" } = 13.5 ; ;




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