15 20 27 triangle

Obtuse scalene triangle.

Sides: a = 15   b = 20   c = 27

Area: T = 147.7299482501
Perimeter: p = 62
Semiperimeter: s = 31

Angle ∠ A = α = 33.17114519508° = 33°10'17″ = 0.57989510542 rad
Angle ∠ B = β = 46.84768650693° = 46°50'49″ = 0.81876320397 rad
Angle ∠ C = γ = 99.98216829799° = 99°58'54″ = 1.74550095597 rad

Height: ha = 19.69772643335
Height: hb = 14.77329482501
Height: hc = 10.94329246297

Median: ma = 22.54444006352
Median: mb = 19.41664878389
Median: mc = 11.41327122105

Inradius: r = 4.76554671775
Circumradius: R = 13.70774872647

Vertex coordinates: A[27; 0] B[0; 0] C[10.25992592593; 10.94329246297]
Centroid: CG[12.42197530864; 3.64876415432]
Coordinates of the circumscribed circle: U[13.5; -2.37659644592]
Coordinates of the inscribed circle: I[11; 4.76554671775]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 146.8298548049° = 146°49'43″ = 0.57989510542 rad
∠ B' = β' = 133.1533134931° = 133°9'11″ = 0.81876320397 rad
∠ C' = γ' = 80.01883170201° = 80°1'6″ = 1.74550095597 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 = 15 ; ; b = 20 ; ; c = 27 ; ;

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

p = a+b+c = 15+20+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 * (31-15)(31-20)(31-27) } ; ; T = sqrt{ 21824 } = 147.73 ; ;

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

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 147.73 }{ 15 } = 19.7 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 147.73 }{ 20 } = 14.77 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 147.73 }{ 27 } = 10.94 ; ;

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{ 15**2-20**2-27**2 }{ 2 * 20 * 27 } ) = 33° 10'17" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 20**2-15**2-27**2 }{ 2 * 15 * 27 } ) = 46° 50'49" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 27**2-15**2-20**2 }{ 2 * 20 * 15 } ) = 99° 58'54" ; ;

6. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 147.73 }{ 31 } = 4.77 ; ;

7. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 15 }{ 2 * sin 33° 10'17" } = 13.71 ; ;




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