11 24 27 triangle

Obtuse scalene triangle.

Sides: a = 11   b = 24   c = 27

Area: T = 131.7577352736
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 23.99550988682° = 23°59'42″ = 0.41987934796 rad
Angle ∠ B = β = 62.53303003387° = 62°31'49″ = 1.09113596232 rad
Angle ∠ C = γ = 93.47546007931° = 93°28'29″ = 1.63114395508 rad

Height: ha = 23.95658823156
Height: hb = 10.98797793947
Height: hc = 9.76598039064

Median: ma = 24.94549393665
Median: mb = 16.76330546142
Median: mc = 12.89437969582

Inradius: r = 4.2550237185
Circumradius: R = 13.52548618995

Vertex coordinates: A[27; 0] B[0; 0] C[5.07440740741; 9.76598039064]
Centroid: CG[10.69113580247; 3.25332679688]
Coordinates of the circumscribed circle: U[13.5; -0.82196886]
Coordinates of the inscribed circle: I[7; 4.2550237185]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 156.0054901132° = 156°18″ = 0.41987934796 rad
∠ B' = β' = 117.4769699661° = 117°28'11″ = 1.09113596232 rad
∠ C' = γ' = 86.52553992069° = 86°31'31″ = 1.63114395508 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 = 24 ; ; c = 27 ; ;

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

p = a+b+c = 11+24+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 * (31-11)(31-24)(31-27) } ; ; T = sqrt{ 17360 } = 131.76 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 131.76 }{ 11 } = 23.96 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 131.76 }{ 24 } = 10.98 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 131.76 }{ 27 } = 9.76 ; ;

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{ 11**2-24**2-27**2 }{ 2 * 24 * 27 } ) = 23° 59'42" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 24**2-11**2-27**2 }{ 2 * 11 * 27 } ) = 62° 31'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-11**2-24**2 }{ 2 * 24 * 11 } ) = 93° 28'29" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 131.76 }{ 31 } = 4.25 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 11 }{ 2 * sin 23° 59'42" } = 13.52 ; ;




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