11 25 27 triangle

Acute scalene triangle.

Sides: a = 11   b = 25   c = 27

Area: T = 137.4344302487
Perimeter: p = 63
Semiperimeter: s = 31.5

Angle ∠ A = α = 24.03298638405° = 24°1'47″ = 0.41994002428 rad
Angle ∠ B = β = 67.74113787262° = 67°44'29″ = 1.18223100986 rad
Angle ∠ C = γ = 88.22987574334° = 88°13'44″ = 1.54398823122 rad

Height: ha = 24.98880549976
Height: hb = 10.99547441989
Height: hc = 10.18803187027

Median: ma = 25.43112799521
Median: mb = 16.39435963108
Median: mc = 13.81112273169

Inradius: r = 4.36329937297
Circumradius: R = 13.50664533847

Vertex coordinates: A[27; 0] B[0; 0] C[4.16766666667; 10.18803187027]
Centroid: CG[10.38988888889; 3.39334395676]
Coordinates of the circumscribed circle: U[13.5; 0.41774721955]
Coordinates of the inscribed circle: I[6.5; 4.36329937297]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 155.977013616° = 155°58'13″ = 0.41994002428 rad
∠ B' = β' = 112.2598621274° = 112°15'31″ = 1.18223100986 rad
∠ C' = γ' = 91.77112425666° = 91°46'16″ = 1.54398823122 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 = 11 ; ; b = 25 ; ; c = 27 ; ;

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

p = a+b+c = 11+25+27 = 63 ; ;

2. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 63 }{ 2 } = 31.5 ; ;

3. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 31.5 * (31.5-11)(31.5-25)(31.5-27) } ; ; T = sqrt{ 18888.19 } = 137.43 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 137.43 }{ 11 } = 24.99 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 137.43 }{ 25 } = 10.99 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 137.43 }{ 27 } = 10.18 ; ;

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+27**2-11**2 }{ 2 * 25 * 27 } ) = 24° 1'47" ; ; b**2 = a**2+c**2 - 2ac cos beta ; ; beta = arccos( fraction{ a**2+c**2-b**2 }{ 2ac } ) = arccos( fraction{ 11**2+27**2-25**2 }{ 2 * 11 * 27 } ) = 67° 44'29" ; ; gamma = 180° - alpha - beta = 180° - 24° 1'47" - 67° 44'29" = 88° 13'44" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 137.43 }{ 31.5 } = 4.36 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin alpha } = fraction{ 11 }{ 2 * sin 24° 1'47" } = 13.51 ; ;

8. Calculation of medians

m_a = fraction{ sqrt{ 2 b**2+2c**2 - a**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 27**2 - 11**2 } }{ 2 } = 25.431 ; ; m_b = fraction{ sqrt{ 2 c**2+2a**2 - b**2 } }{ 2 } = fraction{ sqrt{ 2 * 27**2+2 * 11**2 - 25**2 } }{ 2 } = 16.394 ; ; m_c = fraction{ sqrt{ 2 b**2+2a**2 - c**2 } }{ 2 } = fraction{ sqrt{ 2 * 25**2+2 * 11**2 - 27**2 } }{ 2 } = 13.811 ; ;
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